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list","correct":false,"explanation":"A factor list contains numbers that divide the original number exactly, not its multiples. The correct term is “times table”, which lists successive multiples."},{"text":"number line","correct":false,"explanation":"A number line can display many different values, so it is not specifically a list of multiples. Multiples appear in the number’s times table."},{"text":"place value chart","correct":false,"explanation":"A place value chart shows the value of digits in different positions, not multiples. The answers obtained by repeated multiplication form a times table."}]},{"id":"7cb5fa45-9d9d-fc27-04a1-c604f4887b29","cardType":"basic","points":1,"front":"To find multiples of 6, what equal jumps do you count in?","back":"Count in 6s.","mcqOptions":[{"text":"Count in 6s.","correct":true,"explanation":"Successive multiples of 6 are found by repeatedly adding 6, giving 6, 12, 18, 24 and so on."},{"text":"Count in 3s.","correct":false,"explanation":"Counting in 3s includes numbers such as 3 and 9, which are not multiples of 6. Count in 6s to generate only multiples of 6."},{"text":"Count in 12s.","correct":false,"explanation":"Counting in 12s produces only every second multiple of 6, missing values such as 6 and 18. Count in 6s instead."},{"text":"Count in 1s.","correct":false,"explanation":"Counting in 1s lists every whole number rather than specifically generating multiples of 6. Equal jumps of 6 are required."}]},{"id":"30744379-7a14-3784-20c3-34c71df930e7","cardType":"cloze","points":null,"front":"Multiples of a number keep going [ ].","back":"Multiples of a number keep going forever.","mcqOptions":[{"text":"forever","correct":true,"explanation":"Any whole number can be multiplied by larger and larger whole numbers, so there is no greatest multiple and the sequence continues forever."},{"text":"until 100","correct":false,"explanation":"One hundred is not a stopping point for multiples; multiplication can continue using larger whole numbers. Multiples therefore keep going forever."},{"text":"until they repeat","correct":false,"explanation":"Multiples do not cycle back to the beginning because their values continue increasing. There is no final multiple, so they continue forever."},{"text":"only to 1,000","correct":false,"explanation":"One thousand is merely one possible value, not an upper limit. Multiples can be generated beyond any chosen number and therefore continue forever."}]},{"id":"8194defc-83e3-97a5-b4b2-1d2e5136265d","cardType":"basic","points":1,"front":"Which multiple of 6 is between 25 and 35?","back":"30.","mcqOptions":[{"text":"30.","correct":true,"explanation":"The multiples around this interval are 24, 30 and 36. Only 30 is greater than 25 and less than 35."},{"text":"24.","correct":false,"explanation":"Although 24 is a multiple of 6, it lies below 25 and is therefore outside the stated interval. The required multiple is 30."},{"text":"32.","correct":false,"explanation":"Although 32 lies between 25 and 35, it is not divisible by 6. The multiple of 6 in the interval is 30."},{"text":"36.","correct":false,"explanation":"Although 36 is a multiple of 6, it is greater than 35 and therefore outside the stated interval. The required multiple is 30."}]},{"id":"e412d700-22f5-28a1-16f6-66df8db42fb7","cardType":"basic","points":1,"front":"How can you tell whether a whole number is even or odd?","back":"Check the last digit.","mcqOptions":[{"text":"Check the last digit.","correct":true,"explanation":"A whole number is even when its final digit is 0, 2, 4, 6 or 8; otherwise, its final digit makes it odd."},{"text":"Check the first digit.","correct":false,"explanation":"The first digit does not determine parity; for example, 12 is even while 13 is odd. The last digit must be checked."},{"text":"Check the digit sum.","correct":false,"explanation":"Adding the digits is useful for divisibility by 3 or 9, not for deciding parity. Evenness depends only on the last digit."},{"text":"Check the number of digits.","correct":false,"explanation":"Numbers with the same number of digits can have different parity, such as 24 and 25. The last digit determines whether a number is even or odd."}]},{"id":"8a5355d5-6ea1-f0b7-6218-66682beeebf4","cardType":"basic","points":1,"front":"What is the first even multiple of 7?","back":"14.","mcqOptions":[{"text":"14.","correct":true,"explanation":"The multiples of 7 begin 7, 14, 21 and 28. Since 7 is odd and 14 is even, 14 is the first even multiple."},{"text":"7.","correct":false,"explanation":"Seven is the first positive multiple of 7, but it is odd rather than even. The next multiple, 14, is the first even one."},{"text":"21.","correct":false,"explanation":"Twenty-one is a multiple of 7, but it is odd. The earlier multiple 14 is even, making 14 the first even multiple."},{"text":"28.","correct":false,"explanation":"Twenty-eight is even and divisible by 7, but it is not the first such multiple. The smaller even multiple 14 comes before it."}]},{"id":"bb30fa02-7180-db25-7ec3-eb71dad7e1a9","cardType":"cloze","points":null,"front":"A factor divides into a number exactly, with [ ].","back":"A factor divides into a number exactly, with nothing left over.","mcqOptions":[{"text":"nothing left over","correct":true,"explanation":"A factor divides a number to give a whole-number quotient and a remainder of zero, meaning that nothing is left over."},{"text":"one left over","correct":false,"explanation":"A remainder of 1 means the division is not exact, so the divisor is not a factor. A factor leaves nothing left over."},{"text":"some left over","correct":false,"explanation":"Any amount left over is a non-zero remainder, showing that the division is not exact. A factor must leave nothing left over."},{"text":"a decimal left over","correct":false,"explanation":"A decimal result indicates that the division has not produced a whole-number quotient. A factor divides exactly, with nothing left over."}]},{"id":"07eb0d7c-6eeb-964f-fcec-132b91f27aab","cardType":"basic","points":2,"front":"Why is 3 a factor of 18?","back":"$$18 \\div 3 = 6$ exactly.","mcqOptions":[{"text":"$$18 \\div 3 = 6$ exactly.","correct":true,"explanation":"Dividing 18 by 3 gives the whole number 6 with no remainder. This exact division proves that 3 is a factor of 18."},{"text":"$$18 \\div 3 = 5$ exactly.","correct":false,"explanation":"This is an arithmetic error because 18 divided by 3 equals 6, not 5. The exact quotient of 6 proves that 3 is a factor."},{"text":"$$18 \\div 3 = 6$ with remainder 1.","correct":false,"explanation":"The quotient is 6 with no remainder, so adding a remainder of 1 is incorrect. Exact division is what establishes 3 as a factor."},{"text":"$$18 \\times 3 = 54$ exactly.","correct":false,"explanation":"Multiplying 18 by 3 gives a true product but does not test whether 3 divides into 18. The relevant calculation is 18 divided by 3."}]},{"id":"b54f00c5-8160-cd02-8cc2-8a61dbb4d7dc","cardType":"basic","points":1,"front":"Which factor of 12 pairs with 2?","back":"6, because 2 × 6 = 12.","mcqOptions":[{"text":"6, because 2 × 6 = 12.","correct":true,"explanation":"Factors pair together to make the original number when multiplied. Since 2 × 6 = 12, the factor paired with 2 is 6."},{"text":"4, because 2 × 4 = 12.","correct":false,"explanation":"This confuses the factor paired with 3 with the factor paired with 2. Since 2 × 6 = 12, the required factor is 6, not 4."},{"text":"3, because 2 × 3 = 12.","correct":false,"explanation":"Multiplying 2 by 3 gives 6 rather than 12. The matching factor is 6 because 2 × 6 = 12."},{"text":"12, because 2 × 12 = 12.","correct":false,"explanation":"This treats 12 itself as the factor paired with 2, but 2 × 12 = 24. The correct factor is 6 because 2 × 6 = 12."}]},{"id":"df3e310c-824b-6745-c3db-ce23cd20d9da","cardType":"basic","points":1,"front":"Which factor of 12 pairs with 3?","back":"4, because 3 × 4 = 12.","mcqOptions":[{"text":"4, because 3 × 4 = 12.","correct":true,"explanation":"A factor pair multiplies to make the original number. Since 3 × 4 = 12, the factor paired with 3 is 4."},{"text":"3, because 3 × 3 = 12.","correct":false,"explanation":"This incorrectly treats 12 as a square number. Since 3 × 3 = 9, the required factor is 4 because 3 × 4 = 12."},{"text":"6, because 3 × 6 = 12.","correct":false,"explanation":"This confuses the factor paired with 2 with the factor paired with 3. Since 3 × 6 = 18, the correct paired factor is 4."},{"text":"12, because 3 × 12 = 12.","correct":false,"explanation":"This treats 12 itself as the paired factor, but 3 × 12 = 36. The correct factor is 4 because 3 × 4 = 12."}]},{"id":"0a1be502-d19a-d264-04a6-47ea990f24db","cardType":"cloze","points":null,"front":"For 12, 3 is a [ ], but 24 is a [ ].","back":"For 12, 3 is a factor, but 24 is a multiple.","mcqOptions":[{"text":"For 12, 3 is a factor, but 24 is a multiple.","correct":true,"explanation":"Three is a factor because it divides 12 exactly, while 24 is a multiple because it equals 12 multiplied by the whole number 2."},{"text":"For 12, 3 is a multiple, but 24 is a factor.","correct":false,"explanation":"This reverses factors and multiples. Three divides 12 exactly, so it is a factor; 24 equals 12 × 2, so it is a multiple."},{"text":"For 12, 3 is a factor, but 24 is a factor.","correct":false,"explanation":"Although 3 is a factor of 12, 24 cannot divide 12 to give a whole number. Instead, 24 is a multiple because 12 × 2 = 24."},{"text":"For 12, 3 is a multiple, but 24 is a multiple.","correct":false,"explanation":"Although 24 is a multiple of 12, 3 is not. Three is a factor because 12 ÷ 3 = 4, which is a whole number."}]},{"id":"8c04166f-a5de-4d37-39d7-2da763e77930","cardType":"cloze","points":null,"front":"A prime number is bigger than 1 and has exactly [ ]: [ ].","back":"A prime number is bigger than 1 and has exactly two factors: 1 and itself.","mcqOptions":[{"text":"A prime number is bigger than 1 and has exactly two factors: 1 and itself.","correct":true,"explanation":"A prime number has precisely two positive factors: 1 and the number itself. Having no other factors distinguishes prime numbers from composite numbers."},{"text":"A prime number is bigger than 1 and has exactly one factor: itself only.","correct":false,"explanation":"This overlooks that every positive whole number is divisible by 1. A prime has exactly two factors, and these are 1 and the number itself."},{"text":"A prime number is bigger than 1 and has exactly two factors: 2 and itself.","correct":false,"explanation":"This wrongly assumes 2 is a factor of every prime; in fact, all primes except 2 are odd. The two factors are 1 and the number itself."},{"text":"A prime number is bigger than 1 and has exactly three factors: 1, 2 and itself.","correct":false,"explanation":"This gives an extra factor and would exclude odd primes such as 3 and 5. A prime has exactly two factors: 1 and itself."}]},{"id":"1e64787a-0a55-6363-b4e8-e5c672cbef80","cardType":"basic","points":2,"front":"Why is 1 not prime?","back":"It has only one factor.","mcqOptions":[{"text":"It has only one factor.","correct":true,"explanation":"The only positive factor of 1 is 1 itself. Prime numbers must have exactly two distinct factors, 1 and themselves, so 1 is not prime."},{"text":"It has exactly two factors.","correct":false,"explanation":"This gives the defining number of factors for a prime, but 1 has only one factor: 1. Therefore, it does not meet the definition of a prime number."},{"text":"It has no factors.","correct":false,"explanation":"One does have a factor because 1 divides it exactly. Its only factor is 1, whereas a prime number must have exactly two distinct factors."},{"text":"It is an even number.","correct":false,"explanation":"One is odd, not even, and parity is not the reason it is non-prime. It is not prime because it has only one factor."}]},{"id":"90d5a920-c8ae-f0cc-9bfa-f3dc6ebb6565","cardType":"basic","points":1,"front":"What is the only even prime number?","back":"2.","mcqOptions":[{"text":"2.","correct":true,"explanation":"Two has exactly two factors, 1 and 2, so it is prime. Every other even number is divisible by 2 and therefore has additional factors."},{"text":"3.","correct":false,"explanation":"Three is prime but odd, so it does not satisfy both parts of the question. The only even prime is 2, whose factors are 1 and 2."},{"text":"5.","correct":false,"explanation":"Five has exactly two factors and is therefore prime, but it is odd. The only number that is both even and prime is 2."},{"text":"7.","correct":false,"explanation":"Seven is a prime number because its only factors are 1 and 7, but it is odd. The only even prime number is 2."}]},{"id":"68256cae-f57c-5a2a-ff4f-c8d60d5e3627","cardType":"basic","points":2,"front":"Which prime numbers are between 30 and 40?","back":"31 and 37.","mcqOptions":[{"text":"31 and 37.","correct":true,"explanation":"Neither 31 nor 37 has any factors other than 1 and itself. All the other whole numbers strictly between 30 and 40 are composite."},{"text":"31 and 39.","correct":false,"explanation":"Thirty-nine may look prime, but it is divisible by 3 because 3 × 13 = 39. The prime numbers in this interval are 31 and 37."},{"text":"33 and 37.","correct":false,"explanation":"Thirty-three is composite because 3 × 11 = 33. Thirty-seven is prime, but the other prime number between 30 and 40 is 31."},{"text":"31 and 35.","correct":false,"explanation":"Thirty-five is composite because 5 × 7 = 35. Thirty-one is prime, and the other prime number between 30 and 40 is 37."}]},{"id":"4c349d7d-ce35-c4cf-20e7-3d90725f5f52","cardType":"cloze","points":null,"front":"A square number is made by multiplying a number by [ ].","back":"A square number is made by multiplying a number by itself.","mcqOptions":[{"text":"itself","correct":true,"explanation":"A square number is the product of a whole number multiplied by itself. For example, 5 × 5 = 25, so 25 is a square number."},{"text":"the next number","correct":false,"explanation":"Multiplying consecutive numbers produces an oblong or pronic number, not generally a square. A square is formed by multiplying a number by itself, such as 4 × 4."},{"text":"the previous number","correct":false,"explanation":"Multiplying a number by the previous number uses two different factors and does not generally make a square. A square is made by multiplying a number by itself."},{"text":"a different number","correct":false,"explanation":"A product of two different numbers is not the defining form of a square number. A square is specifically formed by multiplying a number by itself."}]},{"id":"afdddc75-c5b8-1f24-a440-e7c80ec71125","cardType":"basic","points":1,"front":"From 18, 20, 22, 25, 28 and 30, which number is square?","back":"25.","mcqOptions":[{"text":"25.","correct":true,"explanation":"A square number is an integer multiplied by itself. Since $5 \\times 5 = 25$, 25 is the only square number in the given list."},{"text":"20.","correct":false,"explanation":"Being even does not make a number square. The correct answer is 25 because $5 \\times 5 = 25$, whereas no integer multiplied by itself equals 20."},{"text":"28.","correct":false,"explanation":"This may be mistaken for a square because it is close to 25, but $28$ is not an integer squared. The correct answer is $25 = 5^2$."},{"text":"30.","correct":false,"explanation":"A multiple of a familiar number is not necessarily square. Although $30$ is divisible by 5, the correct answer is $25$ because $25 = 5^2$."}]},{"id":"4b792fa5-01d4-5724-3933-ecce3b684f75","cardType":"basic","points":1,"front":"From 4, 11, 12, 15, 18, 25 and 29, choose a factor of 20.","back":"4.","mcqOptions":[{"text":"4.","correct":true,"explanation":"A factor divides a number exactly with no remainder. Since $20 \\div 4 = 5$, 4 is a factor of 20."},{"text":"11.","correct":false,"explanation":"Confusing a nearby number with an exact divisor leads to this choice. The correct answer is 4 because $20 \\div 4 = 5$, while 11 leaves a remainder."},{"text":"12.","correct":false,"explanation":"Being a multiple of 4 does not make a number a factor of 20. The correct answer is 4, which divides 20 exactly; 12 does not."},{"text":"25.","correct":false,"explanation":"This confuses factors with numbers related through a shared factor of 5. The correct answer is 4 because it divides 20 exactly, whereas 25 is greater than 20."}]},{"id":"22834286-122a-4233-ebc2-83fa2cb56c78","cardType":"basic","points":2,"front":"A number is odd, a factor of 30, and a multiple of 5. What are the two possible numbers?","back":"5 and 15.","mcqOptions":[{"text":"5 and 15.","correct":true,"explanation":"The factors of 30 that are odd and divisible by 5 are 5 and 15. Both divide 30 exactly and are multiples of 5."},{"text":"2 and 10.","correct":false,"explanation":"Although both numbers are factors of 30, neither is odd, so they fail one condition. The two numbers satisfying all three conditions are 5 and 15."},{"text":"1 and 3.","correct":false,"explanation":"Both numbers are odd factors of 30, but neither is a multiple of 5. The correct pair is 5 and 15, which satisfies every condition."},{"text":"10 and 30.","correct":false,"explanation":"Both numbers are multiples of 5, but 10 and 30 are even rather than odd. The required odd factors and multiples of 5 are 5 and 15."}]},{"id":"bcce105c-134f-e5c6-0aa1-2db024bdbc37","cardType":"basic","points":1,"front":"For an odd total made from two prime numbers, which prime should you try first?","back":"2.","mcqOptions":[{"text":"2.","correct":true,"explanation":"Every prime except 2 is odd, and two odd numbers have an even sum. Therefore an odd total from two primes must include the only even prime, 2."},{"text":"3.","correct":false,"explanation":"Although 3 is prime, it is odd; adding it to another odd prime gives an even total. Try 2 first because it is the only even prime."},{"text":"5.","correct":false,"explanation":"Choosing 5 confuses a familiar prime with the prime needed for parity. Since 5 and every other odd prime sum to an even number, the correct choice is 2."},{"text":"7.","correct":false,"explanation":"Although 7 is prime, it cannot combine with another odd prime to produce an odd total. The correct prime to try is 2, the only even prime."}]},{"id":"16f98885-e35b-1558-666d-ed64c1fce821","cardType":"basic","points":2,"front":"Find two prime numbers with a sum of 21.","back":"2 and 19.","mcqOptions":[{"text":"2 and 19.","correct":true,"explanation":"Both 2 and 19 are prime, and their sum is $2 + 19 = 21$. Because 21 is odd, one of the two primes must be 2."},{"text":"3 and 17.","correct":false,"explanation":"Both numbers are prime, but their sum is $3 + 17 = 20$, not 21. The required pair is 2 and 19, whose sum is 21."},{"text":"5 and 17.","correct":false,"explanation":"Both numbers are prime, but their sum is $5 + 17 = 22$, which is one too large. The correct pair is 2 and 19."},{"text":"7 and 13.","correct":false,"explanation":"Both numbers are prime, but their sum is $7 + 13 = 20$, not 21. The correct pair is 2 and 19 because it totals 21."}]}]}],"examCountdown":{"examDate":"2027-05-14","paperLabel":"Paper 1"},"heading":"Factors and Multiples","title":"Factors and Multiples Flashcards","topbar":{"backHref":"/gcse/maths/ocr/flashcards"},"topicSidebar":"$L38"}]}],"topicId":"c143b359-451d-43f6-a3dc-7c80b9680f94","walled":"$L39"}],"$L3a","$L3b"]