# Factors of 60

Definition of factors of 60: If a number completely divides 60 without leaving a remainder, then that number is called a factor of 60. Thus, we can say that the factors of 60 are the divisors of 60. Here, we will learn about the factors of 60 and the prime factors of 60.

• 60 = 2×2×3×5 is the prime factorization of 60.
• Factors of 60: 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30 and 60.
• Prime factors of 60: 2, 3, and 5.
• Negative factors of 60: -1, -2, -3, -4, -5, -6, -10, -12, -15, -20, -30 and -60.

## What are the factors of 60?

If 60 = a ×b then we know that a and b are the factors of 60 and (a, b) is a pair factor of 60. So let us write the number 60 multiplicatively in all possible ways. We definitely have:

60 = 1×60

60 = 2×30

60 = 3×20

60 = 4×15

60 = 5×12

60 = 6×10

As there are no numbers between 6 and 10 that can divide 60, so we will stop writing 60 multiplicatively right now. So the factors of 60 in pairs are given as follows:

Thus the pair factors of 60 are (1, 60), (2, 30), (3, 20), (4, 15), (5, 12) and (6, 10). As all the numbers appearing in pair factors are the factors of 60, we conclude that the factors of 60 are 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, and 60.

Thus the total number of factors of 60 is twelve.

## Prime Factors of 60

Note that the factors of 60 are 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, and 60. Among those factors, we observe that only 2, 3, and 5 are prime numbers as they do not have any proper divisors.

∴ the prime factors of 60 are 2, 3, and 5.

## Prime Factorization of 60

To get the prime factorisation of 60, we will start dividing 60 by prime numbers. As 60 is an even number, 2 will divide it and we have

60=2×30

Now we will factorise 30. We have 30=2×15.

Since 15=3×5, we finally have

60= 2×30 = 2×2×15 = 2×2×3×5.

Thus, 60=22×3×5 is the prime factorization of 60, where 2, 3 and 5 are prime numbers.

Question: What are the factors of 60?

Video Solution:

## How to find factors of 60?

Now we will determine the factors of 60 by division method. In this method, we will try to find the numbers that can divide 60 with no remainder. See that

60/1=60 and the remainder is 0.

1 and 60 are factors of 60.

60/2=30 and the remainder is 0.

2 and 30 are factors of 60.

60/3=20 and the remainder is 0.

3 and 20 are factors of 60.

60/4=15 and the remainder is 0.

4 and 15 are factors of 60.

60/5=12 and the remainder is 0.

5 and 12 are factors of 60.

60/6=10 and the remainder is 0.

6 and 10 are factors of 60.

Note that no numbers other than the numbers in violet color can divide 60. So the numbers in violet color, that is, 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, and 60 are the complete list of factors of 60.