n","color":"green","label":"multiply","style":"solid"}]},"order":3,"title":"Multiply common factors","description":"The HCF is the product of every prime factor shared by both numbers. Examiner note: 2 x 3 = 6 earns the accuracy mark (A1)."}]}],"generatedAt":"2026-07-21T03:54:12.361Z","modelVersion":"gpt-5.6-terra","explanationVersion":"v3"},"options":[]}],"options":[],"explanation":null,"firstAttemptFullMarks":{"percent":35,"sampleSize":72}},{"id":"d9835050-d2a7-4f75-9563-8c4c849b17a9","revisionId":"254897d0-a96e-4a16-93f8-3b581c1e5fa5","questionNumber":"6","questionType":"LA","specification":"","difficulty":2,"difficultyBand":null,"totalMarks":3,"sourceTitle":"Prime Factors, HCF and LCM","calculatorUse":null,"parts":[{"id":"2b1ec44e-c5d1-48de-a61c-3bc5f317ca11","label":"0","content":"Find the lowest common multiple (LCM) of 120 and 150","markscheme":"- Prime factors of 120: $2, 2, 2, 3, 5$ and 150: $2, 3, 5, 5$ M1\n- Identifies all factors for LCM (e.g., $2 \\times 2 \\times 2 \\times 3 \\times 5 \\times 5$) M1\n- Final answer: 600 A1","marks":3,"order":0,"markingRubric":{"totalMarks":3,"points":[{"id":"p1","marks":1,"description":"Finds prime factors for both 120 and 150.","code":"M"},{"id":"p2","marks":1,"description":"Identifies the correct set of factors to multiply for LCM.","code":"M"},{"id":"p3","marks":1,"description":"Calculates the LCM as 600.","code":"A"}],"finalAnswers":["600"],"generatedAt":"2026-05-07T01:47:16.835Z","modelVersion":"gemini-3-flash-preview"},"explanation":{"methods":[{"id":"prime_factorisation","label":"Prime factorisation","steps":[{"type":"hyper_latex","block":{"nodes":[{"latex":"120=2\\times2\\times2\\times3\\times5"},{"latex":"150=2\\times3\\times5\\times5"}]},"order":1,"title":"Factorise both numbers","description":"Write each number as a product of prime factors. Examiner: correct prime factorisations of both numbers earn M1."},{"type":"hyper_latex","block":{"nodes":[{"latex":"\\mathrm{LCM}=2\\times2\\times2\\times3\\times5\\times5"},{"text":"This uses three 2s, one 3 and two 5s."}]},"order":2,"title":"Choose every factor","description":"Choose the greatest number of copies of each prime factor appearing in either factorisation. Examiner: identifying this complete set of factors earns M1."},{"type":"hyper_latex","block":{"nodes":[{"latex":"2\\times2\\times2\\times3\\times5\\times5=600"},{"latex":"\\mathrm{LCM}=600"}]},"order":3,"title":"Calculate the LCM","description":"Multiply the selected factors. Examiner: evaluating them to 600 earns the final accuracy mark, A1."}]}],"generatedAt":"2026-07-21T04:01:07.654Z","modelVersion":"gpt-5.6-terra","explanationVersion":"v3"},"options":[]}],"options":[],"explanation":null,"firstAttemptFullMarks":{"percent":36,"sampleSize":53}},{"id":"7cc5c01a-d337-4254-af6a-af8e3857a56a","revisionId":"cf0eceee-f87e-4086-ac28-8840da88b4d7","questionNumber":"7","questionType":"LA","specification":"","difficulty":2,"difficultyBand":null,"totalMarks":3,"sourceTitle":"Prime Factors, HCF and LCM","calculatorUse":null,"parts":[{"id":"70bc936a-736a-43b0-a994-80bc40f2b8fd","label":"0","content":"Find the highest common factor (HCF) of 84 and 120","markscheme":"- Prime factors of 84: $2, 2, 3, 7$ and 120: $2, 2, 2, 3, 5$ M1\n- Identifies common factors $2, 2, 3$ M1\n- $2 \\times 2 \\times 3 = 12$ A1","marks":3,"order":0,"markingRubric":{"totalMarks":3,"points":[{"id":"p1","marks":1,"description":"Finds prime factors for both 84 and 120.","code":"M"},{"id":"p2","marks":1,"description":"Identifies the common prime factors as 2, 2, and 3.","code":"M"},{"id":"p3","marks":1,"description":"Calculates the HCF as 12.","code":"A"}],"finalAnswers":["12"],"generatedAt":"2026-05-07T01:47:16.835Z","modelVersion":"gemini-3-flash-preview"},"explanation":{"methods":[{"id":"prime_factorisation","label":"Prime factorisation","steps":[{"type":"hyper_latex","block":{"nodes":[{"latex":"84=2\\times2\\times3\\times7"},{"latex":"120=2\\times2\\times2\\times3\\times5"}]},"order":0,"title":"Factorise each

Prime Factors, HCF and LCM Questions

Prime Factors, HCF and LCM Questions

Prime Factors, HCF and LCM Questions

Prime Factors, HCF and LCM Questions