# 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.

We know that the divisors of 100 are 1, 2, 4, 5, 10, 20, 25, 50, and 100. So the sum of the divisors of 100 is

= 1+2+4+5+10+20+25+50+100

= 217.

We know that the formula for the product of the divisors of N is as follows:

As 100 has 9 divisors, we obtain that the product of the divisors of 100 is equal to 109.

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