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

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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.