# Factors of 1 – With Prime Factorization | Easy Guide

Contents

As we know, 1 is neither prime nor a composite number and 1 is the only factor of 1 or itself. In this topic, we will learn to prove that 1 has only one factor by some solved examples. Let’s learn some facts about factors of 1.

- Positive Factor of 1: 1
- Negative Factor of 1: -1
- Prime Factorization of 1: As we know that 1 has no prime factors, so we don’t have its prime factorization.
- Sum of Factors of 1: 1

**What Are the Factors of 1?**

In mathematics, the number 1 is called a unit or “unity”. Therefore, the number 1 is neither prime nor composite.

The prime factorization of 1 cannot be achieved because we cannot find factors of 1.

It is more interesting that 1 is a factor of all numbers except 0 (zero).

**Factors of -1**

The factors of -1 appears with only one set, i.e (1 x -1) = -1

**How to Calculate the Factors of 1?**

As we already know 1 is the only factor of 1. Therefore, there are no further factors of 1. In this case, we have to prove that 1 has only one factor, i.e 1.

**Things to Be Noted:**

- 1 is the only factor of 1.
- 1 is the factor of all numbers.
- 1 is the only number whose square and the square root is 1 itself.
- 1 is the identity element for multiplication, i.e. any number multiplied by 1 results in the number itself.

Let’s explore other factors using illustrations and interactive examples. We will see that 1 is

1 and 2.

1, 2, 4, 8, and 16.

1, 2, 3, 4, 6, 8, 12, and 24.

**Factors of 110**

( 1, 2, 5, 10, 11, 22, 55, 110). We have 1, 2, 5, 10, 11, 22, 55, and 110 as factors of 110.

**Factors of 1000**

(1, 2, 4, 5, 10, 20, 25, 50, 100, 125, 200, 250, 500, 1000). We have 1, 2, 4, 5, 10, 20, 25, 50, 100, 125, 200, 250, 500 and 1000

**Factors of 1 by Prime Factorization**

- A prime factorization of 1 is not possible, since it is not a prime number

**Factors of 1 in Pairs**

- In other words, 1 can be found by multiplying 1 by 1, that is, 1 = 1 × 1. The pair factor of 1 is, therefore (1, 1)

**FAQs**

**Is 1 considered a factor?**

Yes, it is true that 1 is the factor of all numbers.

**Is 1 a Prime Factor?**

Since 1 is neither a prime nor a composite number, there are no prime factors of 1. In mathematics, it is called unity or unit.

**Is 1 a Perfect Square?**

Yes. In fact, 1 is the smallest perfect square number in mathematics.

**What Numbers are the Prime Factors of the number 1?**

The prime factorization of number 1 is not possible.

**What is the Greatest Common Factor between number 1 and number X?**

In addition to 1 being a common factor in all numbers, the number 1 has only one factor, which is 1. Therefore, the GCF (Greatest Common Factor) of 1 and any natural number is always 1 i.e. GCF(1, X) = GCF(X, 1) = 1 for all X ∈ ℕ.

**What is the Sum of the Factors of 1?**

In fact, number 1 has only one factor, which is itself. This means that number 1 alone has one factor.