What are the divisors of 5057?

1, 13, 389, 5057

There is a total of 4 positive divisors.
The sum of these divisors is 5460.
The arithmetic mean is 1365.

4 odd divisors

1, 13, 389, 5057

How to compute the divisors of 5057?

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 5057 by each of the numbers from 1 to 5057 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)

5057 / 1 = 5057 (the remainder is 0, so 1 is a divisor of 5057)
5057 / 2 = 2528.5 (the remainder is 1, so 2 is not a divisor of 5057)
5057 / 3 = 1685.6666666667 (the remainder is 2, so 3 is not a divisor of 5057)
...
5057 / 5056 = 1.0001977848101 (the remainder is 1, so 5056 is not a divisor of 5057)
5057 / 5057 = 1 (the remainder is 0, so 5057 is a divisor of 5057)

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 5057 (i.e. 71.112586790244). 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 $\frac{N}{d} = D$ )

5057 / 1 = 5057 (the remainder is 0, so 1 and 5057 are divisors of 5057)
5057 / 2 = 2528.5 (the remainder is 1, so 2 is not a divisor of 5057)
5057 / 3 = 1685.6666666667 (the remainder is 2, so 3 is not a divisor of 5057)
...
5057 / 70 = 72.242857142857 (the remainder is 17, so 70 is not a divisor of 5057)
5057 / 71 = 71.225352112676 (the remainder is 16, so 71 is not a divisor of 5057)