# Prime Factorization

Prime Factorization is the process of expressing a given number as a product of prime factors.

Consider a number say 30. This is a composite number. We can write 30 as

30 = 2 x 15. But 15 is also composite number which can be written as

15 = 3 x 5

∴ 30 = 2 x 3 x 5

When we write 30 = 2 x 3 x 5, none of the numbers 2, 3, 5 are composite numbers.

2, 3, and 5 are prime factors of 30.

Thus we can say that 30 = 2 x 3 x 5 is the prime factorisation of 30.

There are two methods to find the factors of the given numbers.

1) Factor tree

2) Prime Factorisation Method

Factor tree

Example : Factor tree of 72 is given below. Prime Factorisation Method

Another method to find the factors of the given number. Here also use the prime numbers. So start with 2 ,3,5,7 according to divisibility of the number. If we start with 2 then complete the division by 2 and then consider the next prime numbers. Express the following as product of prime factors.

1) 150

150 = 2 x 75

= 2 x 3 x 25

= 2 x 3 x 5 x 5

The prime factors of 150 are 2 x 3 x 5 x 5

2) 732

732 = 2 x 366

= 2 x 2 x 183

= 2 x 2 x 3 x 61
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Practice

Using prime numbers, find the factors of the following :
1) 1331
2) 164
3) 729
4) 180
5) 5000
6) 84
7) 91
8) 105
9) 1000
10) 48

Factors and Multiples

Prime and Composite Numbers
Divisibility rules
Prime factorization
H.C.F or G.C.F
L.C.M
Application on LCM

From prime factorization to Factors and Multiples

Number System