Factors Objective – To be able to find all the factors of a given integer

What is a factor? A factor is; A whole number that divides exactly into another number. e.g. 12 ÷ 3 = 4 so 3 is a factor of 12 Note - 4 is also a factor of 12

Example Q. Find all the factors of 24 Find pairs of numbers that have a product of × 24 = 24 so 1 and 24 are both factors 2 × 12 = 24so 2 and 12 are both factors 3 × 8 = 24 so 3 and 8 are both factors 4 × 6 = 24so 4 and 6 are both factors A. Therefore the factors of 24 are 1,2,3,4,6,8,12 and 24

Question Q. Find all the factors of 16 1 × 16 = 16 2 × 8 = 16 4 × 4 = 16 A. So the factors of 16 are 1,2,4,8 and 16

Exercise Find all the factors of the numbers given; a.12 b.15 c.32 d.36 e.40 f.56

Answers a. 121,2,3,4,6,12 b. 151,3,5,15 c. 321,2,4,8,16,32 d. 361,2,3,4,6,9,12,18,36 e. 401,2,4,5,8,10,20,40 f. 561,2,4,7,8,14,28,56

Plenary All the numbers below have an odd number of factors , 3, , 5, , 2, 3, 4, 6, 9, 12, 18, , 7, , 3, 9, 27, 81 Can you spot anything special about these numbers? Why do they have an odd number of factors? Is it only this type of numbers that has an odd number of factors?

Prime Factors A prime number is a number that has no factors of its own other than itself or 1 5 = 5 X 1Nothing else 13 = 13 X 1Nothing else List all the prime numbers from 2 to 60 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59

A Product of Prime Factors To express a number as a product of prime factors list 2 factors and then see which of these two numbers can be broken down into 2 further factors. Repeat this process until they cannot be broken down any more 12 = 6 X 2 = 3 X 2 X 2

Examples Find the prime factors of = 10 X 2= 5 X 2 X 2 = 12 X 3= 6 X 2 X 3= 3 X 2 X 2 X 3 = 9 X 5= 3 X 3 X 5 = 12 X 5= 6 X 2 X 5= 3 X 2 X 2 X 5

Notes

Q. Find all the factors of 24 Find pairs of numbers that have a product of × 24 = 24 so 1 and 24 are both factors 2 × 12 = 24so 2 and 12 are both factors 3 × 8 = 24 so 3 and 8 are both factors 4 × 6 = 24so 4 and 6 are both factors A. Therefore the factors of 24 are 1,2,3,4,6,8,12 and 24 A factor is; A whole number that divides exactly into another number. e.g. 12 ÷ 3 = 4 so 3 is a factor of 12 Note - 4 is also a factor of 12

Prime Factors A prime number is a number that has no factors of its own other than itself or 1 5 = 5 X 1Nothing else 13 = 13 X 1Nothing else List all the prime numbers from 2 to 60 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59 Find the prime factors of = 10 X 2= 5 X 2 X 2 = 12 X 3= 6 X 2 X 3 = 3 X 2 X 2 X 3 = 9 X 5= 3 X 3 X 5 = 12 X 5= 6 X 2 X 5 = 3 X 2 X 2 X 5