Divisors of 15

The divisors of 15 are those numbers that completely divide 15 with the remainder zero. In this section, we will discuss about divisors of 15.

Highlights of Divisors of 15

  • Divisors of 15: 1, 3, 5 and 15
  • Negative divisors of 15: -1, -3, -5 and -15
  • Prime divisors of 15: 3 and 5
  • Number of divisors of 15: 4
  • Sum of divisors of 15: 24
  • Product of divisors of 15: 152

Also Read:

What are Divisors of 15

A number n is a divisor of 15 if $\frac{15}{n}$ is an integer. Note that if 15/n=m is an integer, then both m and n will be the divisors of 15.

To find the divisors of 15, we need to find the numbers n such that 15/n becomes an integer. We have:

15/1=15 1, 15 are divisors of 15.
15/3=5 3, 5 are divisors of 15

No numbers other than 1, 3, 5 and 15 can divide 15. So we conclude that

The divisors of 15 are:

1, 3, 5 and 15.

Thus, the total number of divisors of 15 is four.

 

Negative Divisors of 15

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

As the divisors of 15 are 1, 3, 5, and 15, we can say that the negative divisors of 15 are -1, -3, -5, and –15.

 

Prime Divisors of 15

The divisors of 15 are 1, 3, 5, and 15. Among these numbers, only 3 and 5 are prime numbers. So we obtain that:

The prime divisors of 15 are 3 and 5.

 

Key Things

The prime factorization of 15 is given below.

15 = 31×51

(i) By the number of divisors formula, we have that the number of divisors of 15 is

=(1+1)(1+1)=2×2=4.

(ii) By the sum of divisors formula, we have that the sum of the divisors of 15 is

$=\frac{3^2-1}{3-1} \times \frac{5^2-1}{5-1}$

$=\frac{9-1}{2} \times \frac{25-1}{4}$

$=4 \times 6=24$

(iii) By the product of divisors formula, we have that the product of the divisors of 15 is

=15(Number of divisors of 15)/3

=154/2

=152

 

Problem Solution on Divisors of 15

Question 1: What is the set of all divisors of 15 in roster form.

Solution:

As the numbers 1, 3, 5, and 15 only can divide 15, we conclude that the set of all divisors of the number 15 in roster form is

{1, 3, 5, 15}

Question 2: Write down the set of all prime divisors of 15 in roster form.

Solution:

We know that the prime numbers 3 and 5 only divide the number 15. Thus, the set of all prime divisors of 15 in roster form is as follows: {3, 5}.