All Divisors of 16

The divisors of 16 are 1, 2, 4, 8, and 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: 2 
• Number of divisors of 16: 5
• Sum of divisors of 16: 31
• Product of divisors of 16: 16^5/2 = 4⁵ =1024.

What are Divisors of 16

A number n is a divisor of 16 if $\dfrac{16}{n}$ 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.

Properties of Divisors of 16

1. The total number of divisors of 16 is five.
2. Using the fact that if m is a divisor of a number, then -m is also a divisor of that number, we conclude that the negative divisors of 16 are -1, -2, -4, -8, and –16.
3. Among the divisors of 16, only 2 is a prime number. So the only prime divisor of 16 is 2.

Sum, Product & Number of Divisors of 16

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

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

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

= 31.

So the sum of divisors of 16 is equal to 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}

=16^5/2 as the number of divisors of 16 is 5.

=4⁵

=1024.

So the product of divisors of 16 is equal to 1024.

Related Topics:

• Divisors of numbers
• Factors of 16
• Square root of 16

Video solution of Divisors of 16:

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}.