FACTORS OF 30 WITH EXAMPLES AND FAQ

## FACTORS OF 30

Any number is a factor of a number if it divides the number without leaving any remainder behind. For example, 2 is a factor of 4, 5 is a factor of 20, etc. 30 is a composite number and hence it has factors that are other than 1 and itself. If a number can completely divide 30 without leaving a remainder, then that number is a factor of 30.

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

Here, 1 is the smallest factor and 30 itself is its biggest factor.

## How to determine factors of 30?

Let’s find the factors by simply dividing 30 by all the numbers starting from 1 to 30 and see which number divides 30 without leaving a remainder. We see that when 30 is divided by 1, 2, 3, 5, 6, 10, 15 and 30 the remainder is 0. Hence 1, 2, 3, 5, 6, 10, 15 and 30 are the factors of 30.

## Prime Factorization of 30

We divide 30 by prime numbers in this method. In this method, we will continue division with the quotient if it’s a composite number till the final quotient is 1. The prime factors can be obtained by (a) Division Method or (b) Factor Tree Method.

(a) Prime Factorization using Division Method

We divide the number 30 by the smallest prime number which doesn’t leave a remainder. The quotient obtained is divided repeatedly by the smallest prime number until the last quotient obtained is 1.

Divide 30 by the prime number 2

30 ÷ 2 = 15, and continue similarly

15 ÷ 3 = 5

5 ÷ 5 = 1

Hence the prime factorization of 30 is 2 × 3 × 5.

(b) Prime Factorization using the Factor Tree Method

We need to find the prime factorization of 30, hence, the root of the factor tree is 30. We can write the pair of factors as the branch of 30. The factor tree ends at a prime factor.

Factor tree of 30

The factor tree ends at 5 since it is a prime number.

∴ Prime factorization of 30 is 2 × 3 × 5.

## Factors of 30 in Pairs

A factor pair includes the set of two numbers whose product will give the number as the product. Factor pairs of 30 are:

1 × 30 = 30, Hence the factor pair is (1, 30).

2 × 15 = 30, Hence the factor pair is (2, 15).

3 × 10 = 30, Hence the factor pair is (3, 10).

5 × 6 = 30, Hence the factor pair is (5, 6).

The product of two negative numbers is positive. The negative factor pairs of 30 are:

(-1) × (-30) = 30, Hence the factor pair is (-1, -30).

(-2) × (-15) = 30, Hence the factor pair is (-2, -15).

(-3) × (-10) = 30, Hence the factor pair is (-3, -10).

(-5) × (-6) = 30, Hence the factor pair is (-5, -6).

## Examples

Example 1: Do 24 and 30 have any factors in common?

Solution: There are seven factors of 24 which are:

24 ÷ 1 = 24

24 ÷ 2 = 12

24 ÷ 3 = 8

24 ÷ 4 = 6

24 ÷ 6 = 4

24 ÷ 12 = 2

24 ÷ 24 = 1

Hence the factors of 24 are 1, 2, 3, 4, 6, 12, and 24 and that of 30 are 1, 2, 3, 5, 6,10, 15 and 30. Therefore, 24 and 30 have 1, 2, 3 and 6 as common factors.

Example 2: Find the sum of all the factors of 30.

Solution:

We know the factors of 30 are 1, 2, 3, 5, 6,10, 15 and 30.

∴ The sum of all the factors is = 1 + 2 + 3 + 5 + 6 + 10 + 15 + 30 = 72.

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Frequently Asked Questions

1. What are the Prime Factors of 30?

Ans: The prime factors are 2, 3 and 5.

2. Determine the Greatest Common Factor of 12 and 30?

Ans: The factors of 12 are 1, 2, 3, 4, 6 and 12 and that of 30 are 1, 2, 3, 5, 6,10, 15 and 30. 12 and 30 have three common factors. The Greatest Common Factor (GCF) of 12 and 30 is 3.

3. How Many Factors of 31 are also common to the Factors of 30?

Ans: 31 is a prime number and hence, 31 and 30 have only one common factor which is 1. Therefore, 31 and 30 are co-prime.