Factors of 60 are the pair of numbers which when multiplied together give the original number. In other words, we can say that, if any number divides 60 completely, then it is the factor of it. Also, as 60 is a composite number, we can derive its prime factors. Apart from 60, there are other numbers such as 24, 12, 18, 12, 48, etc which are composite in nature and have factors of more than 2. The multiples of 60 are the extended times of 60, such as 60, 120, 180, 240, 300, 360, 420, 480, 540 and so on. We can find the factors of a number by the simple multiplication method. It involves the multiplication of a pair of numbers to get another number, say 60. These pair of numbers are the factors. Let us find the factors in pairs for 60, here in this article.

Table of Contents:

• What are the Factors of 60?
• How to find the Factors of 60?
• Pair Factors of 60
• Prime Factorization of 60
• Solved Examples
• FAQs

What are the Factors of 60?

The factors of 60 are the numbers that are multiplied in pairs resulting in the number 60. In other words, the numbers that divide 60 exactly are the factors of 60. The number 60 has more than two factors, as it is a composite number. The factors of 60 are 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30 and 60.

How to Find the Factors of 60?

The steps to find the factors for 60 are given below:

Step 1: First, write the number 60 in your notebook.

Step 2: Find the two numbers, which on multiplication give 60, say 1 and 60, such as 1 × 60 = 60.

Step 3: Let us write another pair of numbers that gives 60 on multiplication, such as 2 and 30, i.e. 2 × 30 = 60.

Step 4: We know that 2 is a prime number with only two factors, i.e. 1 and the number itself. So, we cannot factorize it further.

2 = 1 × 2

Step 5: Now, we need to write another pair such as 3 and 20, i.e. 3 × 20 = 30

Here, 3 is a prime number so we cannot factorise it further.

Step 6: Similarly, we can write other factors as:

4 × 15 = 60

5 × 12 = 60

6 × 10 = 60

12 × 5 = 60

Here, the numbers are repeated in pairs.

Step 7: Therefore, the factors of 60 are 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30 and 60.

Pair Factors of 60

The pair factors of 60 can be positive or negative, but they cannot be decimal or fraction. The pair factor of 60 is the multiplication of two numbers, resulting in the original number 60. The following are the positive and negative pair factors of 60.

Positive Pair Factors of 60:

Negative Pair Factors of 60:

Prime Factorization of 60

The number 60 is a composite number. Now let us find the prime factors of it.

• The first step is to divide the number 60 with the smallest prime factor,i.e. 2.

60 ÷ 2 = 30

• Now, check whether 30 can be further divided by 2 or not.

30 ÷ 2 = 15

15 ÷ 2 = 7.5

          But, factors cannot be a fraction. Therefore, we will proceed to the next prime number, which is 3.

• Now, dividing 15 by 3 we get,

15 ÷ 3 = 5

• Again, dividing 5 by 3 will give a fraction number. Therefore, taking the next prime number, 5, into consideration.

5 ÷ 5 = 1

• We have received 1 at the end and further, we cannot proceed with the division method, as we know that the multiple of 1 is 1, only. So, the prime factorisation of 60 is 2 × 2 × 3 × 5 or it can be written as 2² × 3 × 5. where 2, 3 and 5 are prime numbers.

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Examples

Example 1:

Find the common factors of 60 and 35.

Solution:

The factors of 60 are 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30 and 60 

The factors of 35 are 1, 5, 7 and 35.

Therefore, the common factors of 60 and 35 are 1 and 5.

Example 2:

Find the common factors of 60 and 59.

Solution:

Factors of 60 = 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30 and 60 

Factors of 59 = 1 and 59

Thus, the common factor of 60 and 59 is 1.

Example 3:

Find the common factors of 60 and 30.

Solution:

The factors of 60 are 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30 and 60 

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

Hence, the common factors of 60 and 30 are 1, 2, 3, 5, 6, 10, 15 and 30.

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