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Factor tree Method

In this method, we write pairs of factors for the given number in circles which make
branches of a factor tree.

example 2: Find the prime factorisation of 48 by using factor tree method.

Solution: We can prime factorise the number 48 by using factor tree method as
explained below. 48

Step 1: Start with any comfortable pair of factors 4 × 12
called a factor pair. Here, 4 × 12 = 48
2 × 2 4 × 3
Step 2: If the number at the end of a branch is prime,
2 × 2
we circle it and stop working at that branch. 48 = 2 × 2 × 2 × 2 × 3
Step 3: If the number at the end of the branch is

composite, we continue till the end of each branch is a prime

number and circled.

Step 4: The product of all the circled numbers is the required prime
factorisation of the given number.

Note
 In a factor tree, we can use box to represent a composite number.
 Different factor trees can be made for a given number.

Alternatively,

Step 1: Find two factors such that one is the smallest prime number.

Step 2: Circle the smallest prime factor and work on the 48
other factor (branch) if it is not prime (composite). 2 × 24

Step 3: Continue the process till the numbers at the end of
2 × 12
each branch is circled.
2 × 6
Step 4: Product of all the circled factors is the required
2 × 3
prime factorisation of the given number.

Division Method

Divide the given numbers by the smallest prime number. Continue the division until
it is not further divisible. Division stops when we reach a prime number.

100 Mathematics-4