Definition of factors of 23: If a number completely divides 23 with the remainder zero, then that number is called a factor of 23.
By the above definition, we can say that the factors of 23 are the divisors of 23. In this section, we will learn about the factors of 23 and the prime factors of 23.
Also Read: Basic concepts of the factors of a number
Highlights of Factors of 23
- 23=1×23 is the prime factorization of 23.
- The factors of 23 are 1 and 23.
- The only prime factor of 23 is 23.
- Negative factors of 23 are –1 and –23.
What are the Factors of 23?
To get the factors of 23 we need to first write the number 23 multiplicatively in all possible ways. We have:
23 = 1×23
This is the only way we can express 23 multiplicatively. Therefore the factors of 23 in pairs are given as follows:
|23 = a×b||Factors in Pairs (a,b)|
|23 = 1×23||(1, 23)|
Thus the only pair factor of 23 is (1, 23). We know that all the numbers appearing in pair factors are the factors of 23. So we conclude that
The factors of 23 are:
1 and 23.
Number of Factors of 23
From above we have calculated the factors of 23 which are 1 and 23. Thus the total number of factors of 23 is two.
Prime Factors of 23
Note that the factors of 23 are 1 and 23. Among those factors, we observe that only 23 is a prime number as it does not have any proper divisors.
∴ the only prime factor of 23 is the number 23 itself.
Question: What are the factors of 23?
Video Solution: coming soon…
Is 23 a Prime Number?
As the factors of 23 are 1 and the number itself, by the definition of prime numbers, we can say that 23 is a prime number.
Conclusion: 23 is a prime number.
How to Find Factors of 23?
Now we will determine the factors of 23 by division method. In this method, we will find the numbers that can divide 23 with no remainder. See that
23/1=23 and the remainder is 0.
∴ 1 and 23 are factors of 23.
Note that no numbers other than the numbers in violet color can divide 23. So the numbers in violet color, that is, 1 and 23 are the complete list of factors of 23.