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.