# Divisors of 10

The divisors of 10 are those numbers that completely divide 10 with the remainder zero. In this section, we will discuss about divisors of 10.

## Highlights of Divisors of 10

• Divisors of 10: 1, 2, 5 and 10
• Negative divisors of 10: -1, -2, -5 and -10
• Prime divisors of 10: 2 and 5
• Number of divisors of 10: 4
• Sum of divisors of 10: 18
• Product of divisors of 10: 102

## What are Divisors of 10

A number n is a divisor of 10 if $\frac{10}{n}$ is an integer. Note that if 10/n=m is an integer, then both m and n will be the divisors of 10.

We have:

 10/1=10 1, 10 are divisors of 10. 10/2=5 2, 5 are divisors of 10

No numbers other than 1, 2, 5, and 10 can divide 10. So we conclude that

 The divisors of 10 are: 1, 2, 5 and 10.

Thus, the total number of divisors of 10 is four.

## Negative Divisors of 10

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

As the divisors of 10 are 1, 2, 5 and 10, we can say that the negative divisors of 10 are -1, -2, -5 and –10.

## Prime Divisors of 10

The divisors of 10 are 1, 2, 5 and 10. Among these numbers, we see that 2 and 5 are prime numbers. So we obtain that:

The prime divisors of 10 are 2 and 5.

Key Things

The prime factorization of 10 is given below.

10 = 21×51

(i) By the number of divisors formula, we have that the number of divisors of 10 is

=(1+1)(1+1)=2×2=4.

(ii) By the sum of divisors formula, we have that the sum of the divisors of 10 is

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

$=\frac{4-1}{1} \times \frac{25-1}{4}$

$=3 \times 6=18$

(iii) By the product of divisors formula, we have that the product of the divisors of 10 is

=10(Number of divisors of 10)/2

=104/2

=102

## FAQs on Divisors of 10

Q1: What are the divisors of 10?

Ans: The divisors of 10 are 1, 2, 5, and 10. The negative divisors of 10 are -1, -2, -5, and -10.

Q2: What are the prime divisors of 10?

Ans: The prime divisors of 10 are 2 and 5.

Q3: Find the sum of divisors of 10.

Ans: The sum of divisors of 10 is 1+2+5+10=18.

Q4: What is the greatest common divisor (GCD) of 8 and 10?

Ans: The divisors of 8 are 1, 2, 4, and 8. And the divisors of 10 are 1, 2, 5, and 10. So 2 is the greatest common divisor of 8 and 10.