# Divisors of 25

The divisors of 25 are those numbers that completely divide 25 with the remainder zero. In this section, we will discuss about divisors of 25.

#### Highlights of Divisors of 25

• Divisors of 25: 1, 5 and 25
• Negative divisors of 25: -1, -5 and -25
• Prime divisors of 25: 5
• Number of divisors of 25: 3
• Sum of divisors of 25: 31
• Product of divisors of 25: 253/2 =125.

#### What are Divisors of 25

A number n is a divisor of 25 if $\frac{25}{n}$ is an integer. Note that if 25/n=m is an integer, then both m and n will be the divisors of 25.

To find the divisors of 25, we need to find the numbers n such that 25/n becomes an integer. We have:

 25/1=25 1, 25 are divisors of 25. 25/5=5 5 is a divisor of 25

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

 The divisors of 25 are: 1, 5 and 25.

Thus, the total number of divisors of 25 is three.

#### Negative Divisors of 25

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

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

The negative divisors of 25 are -1, -5, and –25.

#### Prime Divisors of 25

The divisors of 25 are 1, 5, and 25. Among these numbers, only 5 is a prime number. So we obtain that:

The only prime divisor of 25 is 5.

Key Things

The prime factorization of 25 is given below.

25 = 52

(i) By the number of divisors formula, we have that the number of divisors of 25 is

=(2+1)=3.

(ii) By the sum of divisors formula, we have that the sum of the divisors of 25 is

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

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

$=31$

(iii) By the product of divisors formula, we have that the product of the divisors of 25 is

=25(Number of divisors of 25)/2

=253/2

=125

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