Definition of factors of 41: If a number completely divides 41 with the remainder zero, then that number is called a factor of 41. So we can say that the factors of 41 are the divisors of 41. In this section, we will learn about the factors of 41 and the prime factors of 41.
Table of Contents
Highlights of Factors of 41
- 41=1×41 is the prime factorization of 41.
- The factors of 41 are 1 and 41.
- The only prime factor of 41 is 41.
- Negative factors of 41 are -1 and -41.
What are the Factors of 41?
To get the factors of 41 we need to first write the number 41 multiplicatively in all possible ways. We have:
|41 = 1×41||1, 41 are factors of 41|
This is the only way we can express 41 multiplicatively. Note that the factors of 41 are the numbers in brown color. So 1 and 41 are the factors of 41.
We know that if m is a factor of 41 then -m is also a factor of 41. So the negative factors of 41 are -1 and -41.
Pair Factors of 41
|41 = a×b||Pair Factors of 41|
|41 = 1×41||(1, 41)|
Thus the only positive pair factor of 41 is (1, 41). If (m, n) is a positive pair factor then (-m, -n) is a negative pair factor. So (-1, -41) is the only negative pair factor of 41.
Number of Factors of 41
From above we have calculated the factors of 41 which are 1 and 41. Thus the total number of factors of 41 is two.
Prime Factors of 41
Note that the factors of 41 are 1 and 41. Among those factors, we observe that only 41 is a prime number as it does not have any proper divisors.
∴ the only prime factor of 41 is the number 41 itself.
Question: What are the factors of 41?
Video Solution: coming soon…
Is 41 a Prime Number?
As the factors of 41 are 1 and the number itself, by the definition of prime numbers, we can say that 41 is a prime number.
Conclusion: 41 is a prime number.
How to Find Factors of 41?
Now we will determine the factors of 41 by division method. In this method, we will find the numbers that can divide 41 with no remainder. See that
|41/1=41 and the remainder is 0||∴ 1 and 41 are factors of 41|
Note that no numbers other than the numbers in violet color can divide 41. So the numbers in violet color, that is, 1 and 41 are the complete list of factors of 41.