Divisors of 30

The divisors of 30 are those numbers that completely divide 30 with the remainder zero. In this section, we will discuss about 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 $\frac{30}{n}$ 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 we conclude that

The divisors of 30 are:

1, 2, 3, 5, 6, 10, 15 and 30.

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

 

Negative Divisors of 30

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, we can say that:

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

 

Prime Divisors of 30

The divisors of 30 are 1, 2, 3, 5, 6, 10, 15, and 30. Among these numbers, only 2, 3, and 5 are prime numbers. So we obtain that:

The prime divisors of 30 are 2, 3, and 5.

 

Key Things

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

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

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

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

(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

=308/2

=304

Related Topics

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

Q1: What are the divisors of 30?

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

Q2: What are the prime divisors of 30?

Answer: 2, 3, 5 are the prime divisors of 30.

Q3: Find the sum of divisors of 30.

Answer: The sum of the divisors of 30 is = (21+1 – 1)/(2-1) × (31+1 – 1)/(3-1) × (51+1 – 1)/(5-1) = 72.