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Factor Tree Method

In this method, we write pairs of factors for the given number in circles/boxes 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,

we circle it and stop working at that branch. 2 × 2
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.

Step 4: Product of all the circled factors is the required 2 × 6

prime factorisation of the given number. 2 × 3
Division Method 48 = 2 × 2 × 2 × 2 × 3

Divide the given numbers by the smallest prime number. Continue the division until

it is not further divisible. Division stops when we reach to the quotient as a prime
number.

Mathematics-4 101