What are the divisors of 5041?

1, 71, 5041

There is a total of 3 positive divisors.
The sum of these divisors is 5113.
The arithmetic mean is 1704.3333333333.

3 odd divisors

1, 71, 5041

How to compute the divisors of 5041?

A number N is said to be divisible by a number M (with M non-zero) if, when we divide N by M, the remainder of the division is zero.

$N mod M = 0$

Brute force algorithm

We could start by using a brute-force method which would involve dividing 5041 by each of the numbers from 1 to 5041 to determine which ones have a remainder equal to 0.

$Remainder = N - (M \times ⌊ \frac{N}{M} ⌋)$

(where $⌊ \frac{N}{M} ⌋$ is the integer part of the quotient)

5041 / 1 = 5041 (the remainder is 0, so 1 is a divisor of 5041)
5041 / 2 = 2520.5 (the remainder is 1, so 2 is not a divisor of 5041)
5041 / 3 = 1680.3333333333 (the remainder is 1, so 3 is not a divisor of 5041)
...
5041 / 5040 = 1.0001984126984 (the remainder is 1, so 5040 is not a divisor of 5041)
5041 / 5041 = 1 (the remainder is 0, so 5041 is a divisor of 5041)

Improved algorithm using square-root

However, there is another slightly better approach that reduces the number of iterations by testing only integers less than or equal to the square root of 5041 (i.e. 71). Indeed, if a number N has a divisor D greater than its square root, then there is necessarily a smaller divisor d such that:

$D \times d = N$

(thus, if $\frac{N}{D} = d$ , then $\frac{N}{d} = D$ )

5041 / 1 = 5041 (the remainder is 0, so 1 and 5041 are divisors of 5041)
5041 / 2 = 2520.5 (the remainder is 1, so 2 is not a divisor of 5041)
5041 / 3 = 1680.3333333333 (the remainder is 1, so 3 is not a divisor of 5041)
...
5041 / 70 = 72.014285714286 (the remainder is 1, so 70 is not a divisor of 5041)
5041 / 71 = 71 (the remainder is 0, so 71 and 71 are divisors of 5041)