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

Can you… If not you need 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) 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 If not you need

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

Practice 1: Find the prime factors of the following: (the first one is done for you!) 18 The 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. 32 25 72 65 14 Lesson

Practice 2: Write the following as products of their prime factors (the first one is done again!) 36 = 2  18 = 2  2  9 = 2  2  3  3 = 22  32 24 64 56 100 124 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. Lesson

TAIL 1 1 2 3 4 5 6 7 8 9 10 Are you ready for the answers ? Write one factor of 12 1, 2, 3, 4, 6, 12 2, 3 Write one prime factor of 12 Write the 2nd multiple of 8 16 Give two common multiples of 6 and 8 24, 48, 72, etc. Write two factors of 16 1, 2, 4, 8, 16 Write the 4th and 9th multiple of 6 24, 72 Write 40 as a product of its prime factors 2  2  2  5 Write all the factors of 6 1, 2, 3, 6 Give all the common factors of 6 and 8 1, 2 Write 15 as a product of its prime factors Lesson 3  5

Practice 3: Find the highest common factors of the following pairs of numbers (check out the first one!) 12 and 16 12 = 2  6 16 = 2  8 = 2  2  3 = 2  2  4 = 2  2  2  2 HCF = 2  2 = 4 8 and 12 32 and 40 21 and 33 72 and 84 120 and 136 The HCF is found by finding the product of prime factors then looking for the common factors and multiplying them! Lesson

Practice 4: Find the lowest common multiple of the following pairs of numbers (look at number 1 first!) 18 and 24 18 = 2  9 24 = 2  12 = 2  3  3 = 2  2  6 = 2  2  2  3 LCM = 24  3 = 72 25 and 35 10 and 12 8 and 12 16 and 22 15 and 42 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! Lesson

TAIL 2 Are you ready for the answers ? 12 Find the HCF of 24 and 36 Find the LCM of 24 and 32 Find the HCF and LCM of 72 and 120 Write 720 as a product of its prime factors. Hence, or otherwise, find the HCF and LCM of 720 and 84. Express 840 as a product of its prime factors and write the answer in index form. (2) 96 HCF = 24, LCM = 360 24  32  5 HCF = 12 LCM = 5040 (5) 23  3  5  7 Lesson