Definition of factors of 31: If a number completely divides 31 with the remainder zero, then that number is called a factor of 31.
By the above definition, we can say that the factors of 31 are the divisors of 31. In this section, we will learn about the factors of 31 and the prime factors of 31.
Highlights of Factors of 31
- 31=1×31 is the prime factorization of 31.
- The factors of 31 are 1 and 31.
- The only prime factor of 31 is 31.
- Negative factors of 31 are –1 and –31.
What are the Factors of 31?
To get the factors of 31 we need to first write the number 31 multiplicatively in all possible ways. We have:
31 = 1×31
This is the only way we can express 31 multiplicatively. Therefore the factors of 31 in pairs are given as follows:
|31 = a×b||Pair Factors of 31|
|31 = 1×31||(1, 31)|
Thus the only pair factor of 31 is (1, 31). We know that all the numbers appearing in pair factors are the factors of 31. So we conclude that
The factors of 31 are:
1 and 31.
Number of Factors of 31
From above we have calculated the factors of 31 which are 1 and 31. Thus the total number of factors of 31 is two.
Prime Factors of 31
Note that the factors of 31 are 1 and 31. Among those factors, we observe that only 31 is a prime number as it does not have any proper divisors.
∴ the only prime factor of 31 is the number 31 itself.
Question: What are the factors of 31?
Video Solution: coming soon…
Is 31 a Prime Number?
As the factors of 31 are 1 and the number itself, by the definition of prime numbers, we can say that 31 is a prime number.
Conclusion: 31 is a prime number.
How to Find Factors of 31?
Now we will determine the factors of 31 by division method. In this method, we will find the numbers that can divide 31 with no remainder. See that
31/1=31 and the remainder is 0.
∴ 1 and 31 are factors of 31.
Note that no numbers other than the numbers in violet color can divide 31. So the numbers in violet color, that is, 1 and 31 are the complete list of factors of 31.