What are the divisors of 5061?

1, 3, 7, 21, 241, 723, 1687, 5061

There is a total of 8 positive divisors.
The sum of these divisors is 7744.
The arithmetic mean is 968.

8 odd divisors

1, 3, 7, 21, 241, 723, 1687, 5061

How to compute the divisors of 5061?

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 5061 by each of the numbers from 1 to 5061 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)

5061 / 1 = 5061 (the remainder is 0, so 1 is a divisor of 5061)
5061 / 2 = 2530.5 (the remainder is 1, so 2 is not a divisor of 5061)
5061 / 3 = 1687 (the remainder is 0, so 3 is a divisor of 5061)
...
5061 / 5060 = 1.0001976284585 (the remainder is 1, so 5060 is not a divisor of 5061)
5061 / 5061 = 1 (the remainder is 0, so 5061 is a divisor of 5061)

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 5061 (i.e. 71.14070564733). 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 $\frac{N}{d} = D$ )

5061 / 1 = 5061 (the remainder is 0, so 1 and 5061 are divisors of 5061)
5061 / 2 = 2530.5 (the remainder is 1, so 2 is not a divisor of 5061)
5061 / 3 = 1687 (the remainder is 0, so 3 and 1687 are divisors of 5061)
...
5061 / 70 = 72.3 (the remainder is 21, so 70 is not a divisor of 5061)
5061 / 71 = 71.281690140845 (the remainder is 20, so 71 is not a divisor of 5061)