PRIME FACTORS OF 12 WITH EXAMPLES AND FAQ

PRIME FACTORS OF 12

12 is a composite number and hence it has factors that are other than 1 and itself. Factors of 12 are numbers such that when 12 is divided by that number it gives a zero remainder. 12’s factors are 1, 2, 3, 4, 6, and 12. Here, 1 is the smallest factor, 12 itself is its biggest factor and 2, 3 are the prime factors.

What are the factors of any number?

Any number can be a factor of a number if it divides the number without leaving any remainder behind i.e., the remainder is zero. For example, 2 is a factor of 4, 7 is a factor of 21, etc.

How to determine factors of 12?

1. Factors of 12 by Division Method

Let’s find the factors by simply dividing 12 by all the numbers starting from 1 to 12 and see which number divides 12 without leaving a remainder. We see that when 12 is divided by 1, 2, 3, 4, 6, and 12 the remainder is 0. Hence 1, 2, 3, 4, 6, and 12 are the factors of 12.

2. Factors by Prime Factorization Method 

We divide 12 by prime numbers in this method. In this method, we will continue division with the quotient if it’s a composite number till it doesn’t leave a remainder. The prime factors can be obtained by (a) Division Method or (b) Factor Tree Method.

2a. Prime Factorization of 12 by Division Method

We divide the number 12 by the smallest prime number which doesn’t leave a remainder. The quotient obtained is divided repeatedly by the smallest prime number until 0 remainder is obtained.

Divide 12 by the prime number 2 

12 ÷ 2 = 6, and continue similarly

6 ÷ 2 = 3

3 ÷ 3 = 1

Hence the prime factorization of 12 is 2×2×3.

2b. Prime Factorization of 12 by the Factor Tree Method

We need to find the prime factorization of 12, hence, the root of the factor tree is 12. We can take the pair of factors as the branch of 12. The factor tree ends at a prime factor. 

The factor tree ends at 3 since it is a prime number.

Therefore  prime factorization of 12 is 2 \times 2 \times 3=2^{2} \times 3

Prime Factors of 12

Prime factorization of 12 is  2 \times 2 \times 3

The prime factors of 12 are 2 and 3

Examples

Example 1: Do 10 and 12 have any factors in common?

Solution: There are four factors of 10 which are:

10 ÷ 1 = 10

10 ÷ 2 = 5

10 ÷ 5 = 2

10 ÷ 10 = 1

Hence the factors of 10 are 1, 2, 5 and 10 and that of 12 are 1, 2, 3, 4, 6, and 12. Therefore, 10 and 12 have just 1 and 2 as common factors.

Example 2:  Find the sum of all the factors of 12.

Solution:

We know that 12’s factors are 1, 2, 3, 4, 6, and 12.

∴ the sum of all the factors is = 1 + 2 + 3 + 4 + 6 + 12 = 28