# Divisors of 16

The divisors of 16 are those numbers that completely divide 16 without a remainder. In this section, we will discuss about divisors of 16.

#### Highlights of Divisors of 16

• Divisors of 16: 1, 2, 4, 8 and 16
• Negative divisors of 16: -1, -2, -4, -8 and -16
• Prime divisors of 16:
• Number of divisors of 16: 5
• Sum of divisors of 16: 31
• Product of divisors of 16: 165/2 = 45 =1024.

#### What are Divisors of 16

A number n is a divisor of 16 if $\frac{16}{n}$ is an integer. Note that if 16/n=m is an integer, then both m and n will be the divisors of 16.

To find the divisors of 16, we need to find the numbers n such that 16/n becomes an integer. We have:

 16/1=16 1, 16 are divisors of 16. 16/2=8 2, 8 are divisors of 16 16/4=4 4 is a divisor of 16

No numbers other than 1, 2, 4, 8 and 16 can divide 16. So we conclude that

 The divisors of 16 are: 1, 2, 4, 8 and 16.

Thus, the total number of divisors of 16 is five.

#### Negative Divisors of 16

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

As the divisors of 16 are 1, 2, 4, 8, and 16, we can say that:

The negative divisors of 16 are -1, -2, -4, -8, and –16.

#### Prime Divisors of 16

The divisors of 16 are 1, 2, 4, 8, and 16. Among these numbers, only 2 is a prime number. So we obtain that:

The only prime divisor of 16 is 2.

Key Things

The prime factorization of 16 is given below.

16 = 24

(i) By the number of divisors formula, we have that the number of divisors of 16 is

=(4+1)=5.

(ii) By the sum of divisors formula, we have that the sum of the divisors of 16 is

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

$=\frac{32-1}{1}$

$=31$

(iii) By the product of divisors formula, we have that the product of the divisors of 16 is

=16(Number of divisors of 16)/2

=165/2

=45

=1024

 Related Topics

#### Problem Solution on Divisors of 16

Question 1: What is the set of all divisors of 16 in roster form.

Solution:

Note that only 1, 2, 4, 8, and 16 divide the number 16. Thus the set of all divisors of 16 in roster form is given as follows:

{1, 2, 4, 8, 16}.

Question 2: What is the set of all prime divisors of 16 in roster form.

Solution:

Only the prime number 2 can divide the number 16. Thus, the set of all prime divisors of 16 in roster form is the singleton set {2}.