Divisors of 30

The divisors of 30 are 1, 2, 3, 5, 6, 10, 15, and 30. The divisors of 30 are those numbers that completely divide 30 with the remainder zero. In this post, we will discuss divisors of 30.

Highlights of Divisors of 30

• Divisors of 30: 1, 2, 3, 5, 6, 10, 15 and 30
• Negative divisors of 30: -1, -2, -3, -5, -6, -10, -15 and -30
• Prime divisors of 30: 2, 3 and 5
• Number of divisors of 30: 8
• Sum of divisors of 30: 72
• Product of divisors of 30: 30⁴

What are Divisors of 30

A number n is a divisor of 30 if $\dfrac{30}{n}$ is an integer. Note that if 30/n=m is an integer, then both m and n will be the divisors of 30.

To find the divisors of 30, we need to find the numbers n such that 30/n becomes an integer. We have:

30/1=30	1, 30 are divisors of 30.
30/2=15	2, 15 are divisors of 30
30/3=10	3, 10 are divisors of 30
30/5=6	5, 6 are divisors of 30

No numbers other than 1, 2, 3, 5, 6, 10, 15, and 30 can divide 30. So the divisors of 30 are 1, 2, 3, 5, 6, 10, 15, and 30.

Thus, the total number of divisors of 30 is eight.

Properties of Divisors of 30

1. Negative Divisors: We know that if m is a divisor of a number, then -m is also a divisor of that number. As the divisors of 30 are 1, 2, 3, 5, 6, 10, 15, and 30, so the negative divisors of 30 are -1, -2, -3, -5, -6, -10, -15, and –30.
2. Prime Divisors: Among the divisors of 30, only 2, 3, and 5 are prime numbers. So we conclude that the prime divisors of 30 are 2, 3, and 5.

Divisors of 30 Formula

The prime factorization of 30 is given below.

30 = 2¹×3¹×5¹

(i) By the number of divisors formula, we have that the number of divisors of 30 is

=(1+1)(1+1)(1+1)=2×2×2=8.

(ii) By the sum of divisors formula, we have that the sum of the divisors of 30 is

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

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

$=3 \times 4 \times 6=72$

(iii) By the product of divisors formula, we have that the product of the divisors of 30 is

=30^{(Number of divisors of 30)/2}

=30^8/2

=30⁴

Related Topics:

Divisors of Numbers

Divisors of 20

Questions Answers on Divisors of 30

Question 1: Find the GCD of 30 and 45.

Answer:

The divisors of 30 are 1, 2, 3, 5, 6, 10, 15, and 30.

The divisors of 45 are 1, 3, 5, 9, 15, and 45.

So the common divisors of 30 and 45 are 1, 3, 5, and 15. We see that 15 is the greatest number among the common divisors.

Thus we conclude that 15 is the GCD of 30 and 45. That is, GCD(30, 45)=15.

FAQs on Divisors of 30