# Divisors of 12

The divisors of 12 are those numbers that completely divide 12 with the remainder zero. In this section, we will discuss about divisors of 12.

#### Highlights of Divisors of 12

• Divisors of 12: 1, 2, 3, 4, 6 and 12
• Negative divisors of 12: -1, -2, -3, -4, -6 and -12
• Prime divisors of 12: 2 and 3
• Number of divisors of 12: 6
• Sum of divisors of 12: 28
• Product of divisors of 12: 123

#### What are Divisors of 12

A number n is a divisor of 12 if $\frac{12}{n}$ is an integer. Note that if 12/n=m is an integer, then both m and n will be the divisors of 12.

To find the divisors of 12, we need to find the numbers n such that 12/n becomes an integer. We have:

 12/1=12 1, 12 are divisors of 12. 12/2=6 2, 6 are divisors of 12 12/3=4 3, 4 are divisors of 12

So we conclude that

 The divisors of 12 are: 1, 2, 3, 4, 6 and 12.

Thus, the total number of divisors of 12 is six.

#### Negative Divisors of 12

We know that if m is a divisor of a number, then -m is also a divisor of that number.

As the divisors of 12 are 1, 2, 3, 4, 6, and 12, we can say that the negative divisors of 12 are -1, -2, -3, -4, -6, and –12.

#### Prime Divisors of 12

The divisors of 12 are 1, 2, 3, 4, 6, and 12. Among these numbers, only 2 and 3 are prime numbers. So we obtain that:

The prime divisors of 12 are 2 and 3.

Key Things

The prime factorization of 12 is given below.

12 = 22×31

(i) By the number of divisors formula, we have that the number of divisors of 12 is

=(2+1)(1+1)=3×2=6.

(ii) By the sum of divisors formula, we have that the sum of the divisors of 12 is

$=\frac{2^3-1}{2-1} \times \frac{3^2-1}{3-1}$

$=\frac{8-1}{1} \times \frac{9-1}{2}$

$=7 \times 4=28$

(iii) By the product of divisors formula, we have that the product of the divisors of 12 is

=12(Number of divisors of 12)/2

=126/2

=123