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Factor tree method

Š The factor tree method; separate the prime factors in each step.
Š Continue factorisation till all the factors are prime.
example 1: Prime factorise the following numbers using factor tree method.
(a) 24 (b) 36 (c) 56 (d) 108

Solution: (a) 24 (b) 36 Note

1 is not a prime
2 × 12 2 × 18 number and so it
will not appear in
2 × 6 2 × 9 any factor tree.

2 × 3 3 × 3
Therefore, 24 = 2 × 2 × 2 × 3 Therefore, 36 = 2 × 2 × 3 × 3

(c) 56 (d) 108

2 × 28 2 × 54
2 × 27
2 × 14
3 × 9

2 × 7 3 × 3
Therefore, 56 = 2 × 2 × 2 × 7 Therefore, 108 = 2 × 2 × 3 × 3 × 3

division method

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

2. Divide the quotient again by the smallest or the next smallest prime number if it is
not exactly divisible by the smallest prime number.
3. Repeat the process again and again till the quotient becomes 1.
4. Multiply all the prime factors.

example 2: Find the prime factors of the following numbers using division method.
(a) 44 (b) 48 (c) 132

Solution: (a) 2 44 (b) 2 48 (c) 2 132
2 22 2 24 2 66 Remember

11 11 2 12 3 33 Use only prime
2 6
1 3 3 11 11 numbers to divide.
1 1

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

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