# 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 $\frac{100}{n}$ 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 numbers 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.

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 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.

Key Things

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

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

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

$=7 \times 31=217$

(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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