We know that 1 is the first natural number. By definition, the factors of 1 are numbers that divide 1 with the remainder zero. Thus, we can say that the factors of 1 are the divisors of 1. In this section, we will learn about the factors of 1.

**Also Read: **Basic concepts of factors

Table of Contents

## Highlights of Factors of 1

- The only factor of 1 is 1.
- 1 has no prime factors.
- 1 is not a prime number.
- The negative factor of 1 is –1.

## What are the Factors of 1?

To get the factors of 1 we need to first write the number 1 multiplicatively in all possible ways. Note that we have:

1 = 1×1

This is the only way we can express 1 multiplicatively. Therefore the factors of 1 in pairs are given as follows:

1 = a×b | Factors in Pairs (a,b) |

1 = 1×1 | (1, 1) |

Thus the only pair factor of 1 is (1, 1). We know that all the numbers appearing in pair factors are the factors of 1. So we conclude that

The only factor of 1 is 1. |

## Number of Factors of 1

As we see that the only factor of 1 is 1, the total number of factors of 1 is one.

## Prime Factors of 1

Note that the factor of 1 is 1. As we know that 1 is not a prime number, we conclude that:

1 has no prime factors.

Question: What are the factors of 1?

Video Solution: coming soon…

## Is 1 a Prime Number?

By the definition of prime numbers, we know that a prime number has two factors; 1 and the number itself. As 1 has only one factor which is 1, we deduce that 1 is not a prime number.

**Conclusion:** 1 is NOT a prime number.

## How to Find Factors of 1?

Now we will determine the factors of 1 by **division method**. In this method, we will find the numbers that can divide 1 with no remainder. See that

1/1=1 and the remainder is 0.

∴ 1 and 1 are factors of 1. ⇒ 1 is a factor of 1

Note that no numbers other than the numbers in violet color can divide 1. So the numbers in violet color, that is, only 1 is a complete list of factors of 1.

This article is written by Dr. T. Mandal, Ph.D in Mathematics. On Mathstoon.com you will find Maths from very basic level to advanced level. Thanks for visiting.