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Prime Factorisation

It is a way of expressing a number as the product of its prime factors.

Let us consider a number, say 40. It can be expressed as: 40 = 4 × 10. But 4 and 10 both are not
prime numbers. Hence these two numbers need to be factorised again.
4 = 2 × 2 and 10 = 2 × 5. Now the factors of 4 and 10 are prime numbers.

Hence, prime factorisation of 40 = 2 × 2 × 2 × 5, where all the factors are prime numbers. Therefore,
prime factorisation is a method to break down a number into its prime factors which when
multiplied gives the original number.
Does the order matter?

To answer this question, let us count the number of unit blocks in the
given arrangement.
3
We can use any of the ways 2 × 7 × 3 = 42, 2 × 3 × 7 = 42 or 7 × 3 × 2 = 42 to
find the total number of unit blocks. No matter which way we multiply
2, 3, and 7, the result remains the same.

Thus, the order does not matter. Usually we write the prime numbers in 7
increasing order. 2

Note: Every number greater than 1 can be written as a product of prime numbers. The prime factorisation
of a number is unique, except for the order of the factors.

Finding Prime Factorisation

Prime factorisation can be done by: Think and Answer
(a) Division method I am the smallest number,

(b) Factor tree method having four different prime
factors. Can you find me?
Division Method

In this method, a number is successively divided by prime numbers until the quotient becomes
1. Division should be done with the smallest possible prime numbers successively.

Example 9: Find the prime factors of the following by division method

(a) 60 (b) 56 (c) 210

Solution: (a) (b) (c)
2 60 2 56 2 210
2 30 2 28 3 105

3 15 2 14 5 35
5 5 7 7 7 7

1 1 1

60 = 2 × 2 × 3 × 5 56 = 2 × 2 × 2 × 7 210 = 2 × 3 × 5 × 7

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