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

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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