Divisors of 18

The divisors of 18 are those numbers that completely divide 18 without a remainder. In this section, we will discuss about divisors of 18.

Highlights of Divisors of 18

• Divisors of 18: 1, 2, 3, 6, 9 and 18
• Negative divisors of 18: -1, -2, -3, -6, -9 and -18
• Prime divisors of 18: 2 and 3
• Number of divisors of 18: 6
• Sum of divisors of 18: 39
• Product of divisors of 18: 183

What are Divisors of 18

A number n is a divisor of 18 if $\frac{18}{n}$ is an integer. Note that if 18/n=m is an integer, then both m and n will be the divisors of 18.

To find the divisors of 18, we need to find the numbers n such that 18/n becomes an integer. We have:

 18/1=18 1, 18 are divisors of 18. 18/2=9 2, 9 are divisors of 18 18/3=6 3, 6 are divisors of 18

No numbers other than 1, 2, 3, 6, 9 and 18 can divide 18. So we conclude that

 The divisors of 18 are: 1, 2, 3, 6, 9 and 18.

Thus, the total number of divisors of 18 is six.

Negative Divisors of 18

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

As the divisors of 18 are 1, 2, 3, 6, 9, and 18, we can say that:

The negative divisors of 18 are -1, -2, -3, -6, -9, and –18.

Prime Divisors of 18

The divisors of 18 are 1, 2, 3, 6, 9, and 18. Among these numbers, only 2 and 3 are prime numbers. So we obtain that:

The prime divisors of 18 are 2 and 3.

Key Things

The prime factorization of 18 is given below.

18 = 2× 32

(i) By the number of divisors formula, we have that the number of divisors of 18 is

=(1+1)(2+1)=2×3=6.

(ii) By the sum of divisors formula, we have that the sum of the divisors of 18 is

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

$=\frac{4-1}{1} \times \frac{27-1}{2}$

$=3 \times 13=39$

(iii) By the product of divisors formula, we have that the product of the divisors of 18 is

=18(Number of divisors of 18)/2

=186/2

=183

Q1: Find the greatest common divisor of 18 and 24.

Solution:

We know that the divisors of 18 are 1, 2, 3, 6, 9, and 18. Also, the divisors of 24 are 1, 2, 3, 4, 6, 8, 12, and 24.

So the common divisors of 18 and 24 are 1, 2, 3, and 6.

Thus, the greatest common divisor of 18 and 24 is 6.

Q2: Find the set H={x: x is a divisor of 18}.

Solution:

The set H contains the divisors of 18, and we know that the divisors of 18 are 1, 2, 3, 6, 9, and 18.

Thus the set

H={1, 2, 3, 6, 9, 18}.

 Related Topics

FAQs on Divisors of 18

Q1: Find the divisors of 18.

Ans: The divisors of 18 are 1, 2, 3, 6, 9, and 18.

Q2: What are the prime divisors of 18?

Ans: 2 and 3 are the prime divisors of 18.

Q3: Find the sum of the divisors of 18.

Ans: The sum of the divisors of 18 is $=\frac{2^2-1}{2-1} \times \frac{3^3-1}{3-1}$=39.