Divisors of 16 - Mathstoon

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

Table of Contents

Highlights of 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:

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.

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.

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.

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

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

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

$=31$

(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

=4⁵

=1024

Related Topics:

Video solution of 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}.

Share via: