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: 10
^{2}

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## What are Divisors of 10

A number n is a divisor of 10 if $\dfrac{10}{n}$ 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.

Video solution of Divisors of 10:

## Sum, Product & Number of Divisors of 10

The prime factorization of 10 is given below.

10 = 2^{1}×5^{1}

(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

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

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

$=3 \times 6=18$

(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}

=10^{4/2}

=10^{2}

## 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.