# Divisors of 75

The divisors of 75 are those numbers that completely divide 75 with the remainder zero. In this section, we will discuss about divisors of 75.

## Highlights of Divisors of 75

• Divisors of 75: 1, 3, 5, 15, 25 and 75
• Negative divisors of 75:1, -3, -5, -15, -25 and -75
• Prime divisors of 75: 3 and 5
• Number of divisors of 75: 6
• Sum of divisors of 75: 124
• Product of divisors of 75: 753

## What are Divisors of 75

A number n is a divisor of 75 if $\dfrac{75}{n}$ is an integer. Note that if 75/n=m is an integer, then both m and n will be the divisors of 75.

To find the divisors of 75, we need to find the numbers n such that 75/n becomes an integer. We have:

No numbers other than 1, 3, 5, 15, 25, and 75. can divide 75. So we conclude that

Thus, the total number of divisors of 75 is six.

Divisors of 60: The divisors of 60 are 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60.

Divisors of 64: The divisors of 60 are 1, 2, 4, 8, 16, 32, 64.

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

Divisors of 100: The divisors of 100 are 1, 2, 4, 5, 10, 20, 25, 50, 100.

## Negative Divisors of 75

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

As the divisors of 75 are 1, 3, 5, 15, 25, and 75, we can say that:

The negative divisors of 75 are -1, -3, -5, -15, -25, and -75.

## Prime Divisors of 75

The divisors of 75 are 1, 3, 5, 15, 25, and 75. Among these numbers, only 3 and 5 are prime numbers. So we obtain that:

The prime divisors of 75 are 3 and 5.

Video Solution of Divisors of 75:

## Sum, Product & Number of Divisors of 75

The prime factorization of 75 is given below.

75 = 31 × 52

(i) By the number of divisors formula, we have that the number of divisors of 75 is

=(1+1)(2+1)=2×3=6.

(ii) By the sum of divisors formula, we have that the sum of the divisors of 75 is

$=\dfrac{3^2-1}{3-1} \times \dfrac{5^3-1}{5-1}$

$=\dfrac{9-1}{2} \times \dfrac{125-1}{4}$

$=4 \times 31=124$

(iii) By the product of divisors formula, we have that the product of the divisors of 75 is

=75(Number of divisors of 75)/2

=756/2

=753

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## FAQs on Divisors of 75

Q1: Find divisors of 75.

Answer: The divisors of 75 are 1, 3, 5, 15, 25, and 75.

Q2: What is the sum of divisors of 75?

Answer: The sum of the divisors of 75 is (32-1)/(3-1) × (53-1)/(5-1) = 4×31 = 124.

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