Factors of 1

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

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.