# Divisors of 8

The divisors of 8 are those numbers that completely divide 8 with the remainder zero. In this section, we will discuss about divisors of 8.

#### Highlights of Divisors of 8

• Divisors of 8: 1, 2, 4 and 8
• Negative divisors of 8: -1, -2, -4 and -8
• Prime divisors of 8: 2
• Number of divisors of 8: 4
• Sum of divisors of 8: 15
• Product of divisors of 8: 82

#### What are Divisors of 8

A number n is a divisor of 8 if $\frac{8}{n}$ is an integer. Note that if 8/n=m is an integer, then both m and n will be the divisors of 8.

We have:

 8/1=8 1, 8 are divisors of 8. 8/2=4 2, 4 are divisors of 8

No numbers other than 1, 2, 4, and 8 can divide 8. So we conclude that

 The divisors of 8 are: 1, 2, 4 and 8.

Thus, the total number of divisors of 8 is four.

#### Negative Divisors of 8

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

As the divisors of 8 are 1, 2, 4 and 8, we can say that the negative divisors of 8 are -1, -2, -4 and –8.

#### Prime Divisors of 8

The divisors of 8 are 1, 2, 4 and 8. Among these numbers, only 2 is a prime number. So we obtain that:

The only prime divisor of 8 is 2.

Key Things

The prime factorization of 8 is given below.

8 = 23

(i) By the number of divisors formula, we have that the number of divisors of 8 is

=(3+1)=4.

(ii) By the sum of divisors formula, we have that the sum of the divisors of 8 is

$=\frac{2^4-1}{2-1}$

$=\frac{16-1}{1}$

$=15$

(iii) By the product of divisors formula, we have that the product of the divisors of 8 is

=8(Number of divisors of 8)/2

=84/2

=82

#### Question Answer on Divisors of 8

Question 1: Is 3 a divisor of 8?