# what are the factors of 60

## Factors of 60

In mathematics, factors are numbers that can be divided evenly into a given number. In this article, we will explore the factors of 60 and understand how they are derived.

### Introduction to Factors

Factors play a crucial role in various mathematical calculations, including prime factorization, finding common factors, and determining the divisors of a number. Factors are the numbers that divide a given number without leaving a remainder.

### Understanding the Number 60

Before diving into the factors of 60, let’s understand what this number represents. 60 is a positive integer that is divisible by 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, and 60.

### Finding Factors of 60

To find the factors of 60, we need to determine all the numbers that divide 60 without a remainder. Let’s explore the process step by step:

#### Step 1: Dividing by 1

When we divide 60 by 1, we get the result as 60.

#### Step 2: Dividing by 2

Dividing 60 by 2 gives us the result as 30.

#### Step 3: Dividing by 3

On dividing 60 by 3, we get 20 as the result.

#### Step 4: Dividing by 4

When we divide 60 by 4, the result obtained is 15.

#### Step 5: Dividing by 5

Dividing 60 by 5 gives us the result as 12.

#### Step 6: Dividing by 6

On dividing 60 by 6, we obtain 10 as the result.

#### Step 7: Dividing by 10

When we divide 60 by 10, the result obtained is 6.

#### Step 8: Dividing by 12

Dividing 60 by 12 gives us the result as 5.

#### Step 9: Dividing by 15

On dividing 60 by 15, we obtain 4 as the result.

#### Step 10: Dividing by 20

When we divide 60 by 20, the result obtained is 3.

#### Step 11: Dividing by 30

Dividing 60 by 30 gives us the result as 2.

#### Step 12: Dividing by 60

On dividing 60 by 60, we obtain 1 as the result.

### List of Factors

After going through the above steps, we have determined all the factors of 60. These factors are: 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, and 60.

### Importance of Factors

The concept of factors holds great significance in multiple areas of mathematics. These factors help us in finding the greatest common divisor, simplifying fractions, and determining prime numbers. They are also utilized in algebraic equations, number theory, and various other mathematical operations.

### Conclusion

In conclusion, the factors of 60 are the numbers that can evenly divide 60 without leaving any remainder. These factors include 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, and 60. Understanding the factors of a number is essential in various mathematical calculations and problem-solving.