# Multiples, Factors, Primes, Squares and Cubes

MULTIPLES, FACTORS, PRIMES, SQUARES AND CUBES Factors The whole numbers that divide exactly into 20 are called factors of 20. So 4 is a factor of 20 because 20 4 = 5. Examples 1 3 4 5 6 7 8

9 10 11 12 From the set of numbers above write down the numbers that are factors of 48. The numbers that are factors of 48 are 3, 4, 6, 8 and 12. 2 List all the factors of 36. List all the factor pairs. 36 = 1 36 36 = 2 18 36 = 3 12 36 = 4 9 36 = 6 6 Write the factors in order. Factors of 36 = 1, 2, 3, 4, 6, 9, 12, 18, 36

3 Find the highest common factor (HCF) of 27 and 90. List all the factors of each number. Factors of 27 = 1 3 9 27 Factors of 90 = 1 2 3

5 6 9 10 15 18 30 45 90 Select the common factors. The highest common factor of 27 and 90 is 9. Multiples The multiples of 8 are 8, 16, 24, 32, 40, ... The multiples of 13 are 13, 26, 39, 52, ... Examples 1 2

4 7 10 15 20 29 34 44 52 74 From the set of numbers above write down the numbers that are multiples of 4. The numbers that are multiples of 4 are 4, 20, 44 and 52. 2 Find the lowest common multiple (LCM) of 6 and 15. Multiples of 6 = 6 List the multiples of each number. 12 18 24 30 36 42 48 54 60 66 72

Multiples of 15 = 15 30 45 60 75 90 105 120 135 150 165 Select the common multiples. The lowest common multiple of 6 and 15 is 30. Primes A prime number is a number that has exactly two factors. 7 is a prime number because it has exactly two factors (1 and 7). Examples 1 20 21 22 23 24 25 26 27 28 29 30 From the set of numbers above write down the numbers that are prime. The numbers that are prime are 23 and 29. 2 List all the prime factors of 84. List all the factors of 84. Factors of 84 = 1

2 3 4 6 7 12 14 21 28 42 84 Select the factors that are prime. The prime factors of 84 are 2, 3 and 7. 3 Write 42 as the product of its prime factors. 42 42 can be written as 6 7. 7

6 6 can be written as 2 3. 2 3 42 = 2 3 7 4 Write 120 as the product of its prime factors. 120 120 can be written as 10 12. 12 10 10 can be written as 2 5. 12 can be written as 3 4.

2 5 4 3 4 can be written as 2 2. 2 120 = 2 5 3 2 2 2 = 23 3 5 5 Find the highest common factor (HCF) and lowest common multiple (LCM) of 42 and 120. From example 3:

42 = 2 3 7 From example 4: 120 = 2 2 2 3 5 Write the prime factors on the diagram. 7 Prime factors of 42 2 3 2 2

5 Prime factors of 120 The HCF is the product of the numbers in the intersection = 2 3 = 6. The LCM is the product of all the numbers on the diagram = 7 2 3 2 2 5 = 840. Square numbers 11=1 22=4 33=9 4 4 = 16 The numbers 1, 4, 9, 16 are called square numbers. 4 4 can be written as 42.

Example 1 15 32 49 53 62 71 81 94 100 From the set of numbers above write down the numbers that are square numbers. The numbers that are square numbers are 49, 81 and 100. Cube numbers 111=1 3 3 3 = 27 222=8 The numbers 1, 8, 27, 64 are called cube numbers. 4 4 4 can be written as 43. Example 1

1 7 24 25 125 200 216 From the set of numbers above write down the numbers that are cube numbers. The numbers that are cube numbers are 1, 125 and 216.

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