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.

Table of Contents

## 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: 100
^{9/2 }= 10^{9}

## 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:

100/1=100 | 1, 100 are divisors of 100. |

100/2=50 | 2, 50 are divisors of 100 |

100/4=25 | 4, 25 are divisors of 100 |

100/5=20 | 5, 20 are divisors of 100 |

100/10=10 | 10 is a divisor of 100 |

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

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

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

**Also Read:**

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 64 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 75: | The divisors of 75 are 1, 3, 5, 15, 25, 75. |

## 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 = 2^{2} × 5^{2}

(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}

=100^{9/2}

=10^{9}

**Related Topics:**

## Question-Answer on Divisors of 100

**Question 1:** Find the highest divisor of 100.

*Answer*:

100 is the highest divisor of 100.

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

*Answer*:

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:

Product of divisors of N = N^{No. of divisors of N} |

As 100 has 9 divisors, we obtain that the product of the divisors of 100 is equal to 10^{9}.

This article is written by Dr. T. Mandal, Ph.D in Mathematics. On Mathstoon.com you will find Maths from very basic level to advanced level. Thanks for visiting.