36 – ITS FACTORS AND METHODS

FACTORS OF 36

What are the factors? They are the numbers that divide the number completely leaving no remainders. So, factors of 36 are the numbers that divide the number 36 completely and leave no remainder. The factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18 and 36. The factors can be written as ordered pairs as well.

HOW DO WE FIND THE FACTORS OF 36?

There are many methods to find the factors of a number. We will use two methods to find the factors of 36 namely prime factorization by long division method and factor tree method.

PRIME FACTORIZATION USING DIVISION METHOD

The steps to follow for finding factors using the division method are as follow:

1. Find the smallest prime number divisible by the original number so that it leaves no remainder.
2. Now, find the prime factor of the quotient received in step 1 and keep repeating this process till the last number is a prime number.

Look at following prime factorization of 36 –

Therefore, 36 = 2 x 2 x 3 x 3 or

36 = 2² x  3²

PRIME FACTORIZATION USING FACTOR TREE METHOD

As the name suggests, we make a tree with the original number as the root and the factors as branches. We keep on breaking down the composite numbers till we get the prime factors. Let us see through the following diagram about how to find the factors of 36:

Here, we first break 36 as the product of 6

So, 36 = 6 x 6

Now 6 is not a prime number so we break 6 into a prime number.

6 = 2 x 3

36 = 2 x 3 x 2 x 3

36 = 2² x  3²