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\\October 8, 2025 12:13 PM Bharat Arora P-9 Reader _________________________ Date: ___________________74

Factor tree Method

Š Draw a factor tree and separate the prime factors at each step.
Š Continue factorisation till all the factors are prime.

example 1: Prime factorise the following numbers using the factor tree method.
( a) 24 (b) 36 (c) 56 (d) 108

Be Aware
Solution: (a) 24 (b) 36 Since 1 is not prime,
number it is excluded
2 × 12 2 × 18 from any factor trees.

2 × 6 2 × 9

2 × 3 3 × 3
24 = 2 × 2 × 2 × 3 36 = 2 × 2 × 3 × 3

(c) 56 (d) 108

2 × 28 2 × 54
2 × 27
2 × 14
3 × 9
2 × 7 3 × 3

56 = 2 × 2 × 2 × 7 108 = 2 × 2 × 3 × 3 × 3

division Method

To factorise a number using the division method, we follow these steps.
Step 1: Divide the number by the smallest prime number which divides the number exactly.

Step 2: Divide the quotient again by the smallest prime number. If the quotient is not
exactly divisible by the smallest prime number, divide it by the next smallest prime number.

Step 3: Repeat the process till the quotient becomes 1.
Step 4: Multiply all the prime factors.

example 2: Find the prime factors of the following numbers using the division method.

( a) 44 (b) 48 (c) 132

Solution: (a) 2 44 (b) 2 48 (c) 2 132
2 22 2 24 2 66
11 11 2 12 3 33
2 6
1 3 3 11 11

1 1

44 = 2 × 2 × 11 48 = 2 × 2 × 2 × 2 × 3 132 = 2 × 2 × 3 × 11

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