Factors of 1 – With Prime Factorization | Easy Guide

ECTI Pakistan - Factors of 1

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  

Factor of 2

1 and 2.

Prime factorization of 16  

1, 2, 4, 8, and 16.

24 Prime factorization 

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.