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
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What are Divisors of 15
A number n is a divisor of 15 if $\dfrac{15}{n}$ 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.
Sum, Product & Number of Divisors of 15
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
$=\dfrac{3^2-1}{3-1} \times \dfrac{5^2-1}{5-1}$
$=\dfrac{9-1}{2} \times \dfrac{25-1}{4}$
$=4 \times 6=24$
(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
Video solution of Divisors of 15:
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}.