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 $\dfrac{12}{n}$ 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.
Video solution of Divisors of 12:
Sum, Product & Number of Divisors of 12
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
$=\dfrac{2^3-1}{2-1} \times \dfrac{3^2-1}{3-1}$
$=\dfrac{8-1}{1} \times \dfrac{9-1}{2}$
$=7 \times 4=28$
(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