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Targeting Grade C Number Unit 5 Prime Factors, HCF and LCM GCSE Mathematics

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TOP: Review prime numbers, factors, multiples Practice 1: Finding prime factors Practice 2: Expressing numbers as products of prime factors TAIL 1 Practice 3: Finding HCF Practice 4: Finding LCM TAIL 2 Can you… Find prime factors Write a number as a product of its prime factors Try a test Find the Highest Common Factor (HCF) Find the Lowest Common Multiple (LCM) Try a test If not you need

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TOP: (1)From the following list, write down all the prime numbers: 5, 11, 4, 9, 17, 27, 31, 6, 37, 21 (2)Write all the factors of 24. (3)Write the first five multiples of 6. (4)Write all the prime numbers between 40 and 50. (5)Write the common factors of 24 and 36. (6)Write the first three common multiples of 3 and 5. Lesson

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Practice 1: Find the prime factors of the following: (the first one is done for you!) (1)18The factors are 1, 2, 3, 6, 9 and 18 and the prime numbers of this group are 2 and 3, so the prime factors of 18 are 2 and 3. (2)32 (3)25 (4)72 (5)65 (6)14 Lesson

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Practice 2: Write the following as products of their prime factors (the first one is done again!) (1)36 = 2 18 = 2 2 9 = 2 2 3 3 = 2 2 3 2 (2)24 (3)64 (4)56 (5)100 (6)124 Lesson See how the black number is split into a prime factor and other number at each stage, while the prime factors already found are carried down.

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Write one factor of Write one prime factor of 12 Write the 2 nd multiple of 8 Give two common multiples of 6 and 8 Write two factors of 16 Write the 4 th and 9 th multiple of 6 Write 40 as a product of its prime factors Write all the factors of 6 Give all the common factors of 6 and 8 Write 15 as a product of its prime factors 1, 2, 3, 4, 6, 12 2, , 48, 72, etc. 1, 2, 4, 8, 16 24, 72 2 2 2 5 1, 2, 3, 6 1, 2 3 5 Are you ready for the answers ? TAIL 1 Lesson

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Practice 3: Find the highest common factors of the following pairs of numbers (check out the first one!) (1)12 and 1612 = 2 616 = 2 8 = 2 2 3 = 2 2 4 = 2 2 2 2 HCF = 2 2 = 4 (2)8 and 12 (3)32 and 40 (4)21 and 33 (5)72 and 84 (6)120 and 136 Lesson The HCF is found by finding the product of prime factors then looking for the common factors and multiplying them!

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Practice 4: Find the lowest common multiple of the following pairs of numbers (look at number 1 first!) (1)18 and 2418 = 2 924 = 2 12 = 2 3 3 = 2 2 6 = 2 2 2 3 LCM = 24 3 = 72 (2)25 and 35 (3)10 and 12 (4)8 and 12 (5)16 and 22 (6)15 and 42 Lesson The LCM is found by finding the product of prime factors then looking at the common factors and multiplying the biggest number you started with by any additional factors in the smaller number!

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TAIL 2 (1)Find the HCF of 24 and 36 (2)Find the LCM of 24 and 32 (3)Find the HCF and LCM of 72 and 120 (4)Write 720 as a product of its prime factors. Hence, or otherwise, find the HCF and LCM of 720 and 84. (5)Express 840 as a product of its prime factors and write the answer in index form. Lesson (1)12 (2) 96 (3)HCF = 24, LCM = 360 (4)2 4 3 2 5 HCF = 12 LCM = 5040 (5) 2 3 3 5 7 Are you ready for the answers ?

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