# Divisors of 72

The divisors of 72 are 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, and 72. The divisors of 72 are those numbers that completely divide 72 without a remainder. In this section, we will discuss divisors of 72.

## Highlights of Divisors of 72

• Divisors of 72: 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36 and 72.
• Negative divisors of 72:1, -2, -3, -4, -6, -8, -9, -12, -18, -24, -36, and -72.
• Prime divisors of 72: 2 and 3
• Number of divisors of 72: 12
• Sum of divisors of 72: 195
• Product of divisors of 72: 72

## What are Divisors of 72

A number n is a divisor of 72 if $\dfrac{72}{n}$ is an integer. Note that if 72/n=m is an integer, then both m and n will be the divisors of 72.

To find the divisors of 72, we need to find the numbers n such that 72/n becomes an integer. We have:

No numbers other than 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, and 72 can divide 72. So we conclude the following:

The divisors of 72 are 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, and 72.

Thus, the total number of divisors of 72 is twelve.

## Negative Divisors of 72

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

As the divisors of 72 are 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, and 72, we can say that:

The negative divisors of 72 are -1, -2, -3, -4, -6, -8, -9, -12, -18, -24, -36, and -72.

## Prime Divisors of 72

The divisors of 72 are 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, and 72. Among these numbers, only 2 and 3 are prime numbers. So we obtain that:

The prime divisors of 72 are 2 and 3.

Video Solution of Divisors of 72:

## Sum, Product & Number of Divisors of 72

The prime factorization of 72 is given below.

72 = 23 × 32

(i) By the number of divisors formula, we have that the number of divisors of 72 is

=(3+1)(2+1)=4×3=12.

(ii) By the sum of divisors formula, we have that the sum of the divisors of 72 is

$=\dfrac{2^4-1}{2-1} \times \dfrac{3^3-1}{3-1}$

$=\dfrac{16-1}{1} \times \dfrac{27-1}{2}$

= 15 × 13

= 195

(iii) By the product of divisors formula, we have that the product of the divisors of 72 is

=72(Number of divisors of 72)/2

=7212/2

=726

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## FAQs

Q1: What are the divisors of 72?

Answer: 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, and 72 are all divisors of 72.

Q2: What is the sum of divisors of 72?

Answer: Note that 72 = 23 × 32. So the sum of divisors of 72 equals (24-1)/(2-1) ×(33-1)/(3-1) = 15 × 13 = 195.

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