# 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

Number System

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