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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