# Divisors of 100

The divisors of 100 are those numbers that completely divide 100 with the remainder zero. In this section, we will discuss about divisors of 100.

## Highlights of Divisors of 100

• Divisors of 100: 1, 2, 4, 5, 10, 20, 25, 50 and 100
• Negative divisors of 100: -1 -2, -4, -5, -10, -20, -25, -50 and -100
• Prime divisors of 100: 2 and 5
• Number of divisors of 100: 9
• Sum of divisors of 100: 217
• Product of divisors of 100: 1009/2 = 109

## What are Divisors of 100

A number n is a divisor of 100 if $\dfrac{100}{n}$ is an integer. Note that if 100/n=m is an integer, then both m and n will be the divisors of 100.

To find the divisors of 100, we need to find the number n such that 100/n becomes an integer. We have:

No numbers other than 1, 2, 4, 5, 10, 20, 25, 50, and 100 can divide 100. So we conclude that

Thus, the total number of divisors of 100 is nine.

## Negative Divisors of 100

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

As the divisors of 100 are 1, 2, 4, 5, 10, 20, 25, 50, and 100, we can say that:

The negative divisors of 100 are -1, -2, -4, -5, -10, -20, -25, -50, and -100.

## Prime Divisors of 100

The divisors of 100 are 1, 2, 4, 5, 10, 20, 25, 50, and 100. Among these numbers, only 2 and 5 are prime numbers. So we obtain that:

The prime divisors of 100 are 2 and 5.

## Sum, Product & Number of Divisors of 100

The prime factorization of 100 is given below.

100 = 22 × 52

(i) By the number of divisors formula, we have that the number of divisors of 100 is

=(2+1)(2+1)=3×3=9.

(ii) By the sum of divisors formula, we have that the sum of the divisors of 100 is

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

$=\dfrac{8-1}{1} \times \dfrac{125-1}{4}$

$=7 \times 31=217$

(iii) By the product of divisors formula, we have that the product of the divisors of 100 is

=100(Number of divisors of 100)/2

=1009/2

=109

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## Question-Answer on Divisors of 100

Question 1: Find the highest divisor of 100.

100 is the highest divisor of 100.

Question 2: Find the sum and the product of the divisors of 100.