Definition of factors of 37: If a number completely divides 37 with the remainder zero, then that number is called a factor of 37.
By the above definition, we can say that the factors of 37 are the divisors of 37. In this section, we will learn about the factors of 37 and the prime factors of 37.
Also Read: Basic concepts of the factors of a number
Highlights of Factors of 37
- 37=1×37 is the prime factorization of 37.
- The factors of 37 are 1 and 37.
- The only prime factor of 37 is 37.
- Negative factors of 37 are –1 and –37.
What are the Factors of 37?
To get the factors of 37 we need to first write the number 37 multiplicatively in all possible ways. We have:
37 = 1×37
This is the only way we can express 37 multiplicatively. Therefore the factors of 37 in pairs are given as follows:
|37 = a×b||Factors in Pairs (a,b)|
|37 = 1×37||(1, 37)|
Thus the only pair factor of 37 is (1, 37). We know that all the numbers appearing in pair factors are the factors of 37. So we conclude that
The factors of 37 are:
1 and 37.
Number of Factors of 37
From above we have calculated the factors of 37 which are 1 and 37. Thus the total number of factors of 37 is two.
Prime Factors of 37
Note that the factors of 37 are 1 and 37. Among those factors, we observe that only 37 is a prime number as it does not have any proper divisors.
∴ the only prime factor of 37 is the number 37 itself.
Question: What are the factors of 37?
Video Solution: coming soon…
Is 37 a Prime Number?
As the factors of 37 are 1 and the number itself, by the definition of prime numbers, we can say that 37 is a prime number.
Conclusion: 37 is a prime number.
How to Find Factors of 37?
Now we will determine the factors of 37 by division method. In this method, we will find the numbers that can divide 37 with no remainder. See that
37/1=37 and the remainder is 0.
∴ 1 and 37 are factors of 37.
Note that no numbers other than the numbers in violet color can divide 37. So the numbers in violet color, that is, 1 and 37 are the complete list of factors of 37.