What are the divisors of 5177?

1, 31, 167, 5177

There is a total of 4 positive divisors.
The sum of these divisors is 5376.
The arithmetic mean is 1344.

4 odd divisors

1, 31, 167, 5177

How to compute the divisors of 5177?

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 5177 by each of the numbers from 1 to 5177 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)

5177 / 1 = 5177 (the remainder is 0, so 1 is a divisor of 5177)
5177 / 2 = 2588.5 (the remainder is 1, so 2 is not a divisor of 5177)
5177 / 3 = 1725.6666666667 (the remainder is 2, so 3 is not a divisor of 5177)
...
5177 / 5176 = 1.0001931993818 (the remainder is 1, so 5176 is not a divisor of 5177)
5177 / 5177 = 1 (the remainder is 0, so 5177 is a divisor of 5177)

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 5177 (i.e. 71.951372467799). 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 $\frac{N}{d} = D$ )

5177 / 1 = 5177 (the remainder is 0, so 1 and 5177 are divisors of 5177)
5177 / 2 = 2588.5 (the remainder is 1, so 2 is not a divisor of 5177)
5177 / 3 = 1725.6666666667 (the remainder is 2, so 3 is not a divisor of 5177)
...
5177 / 70 = 73.957142857143 (the remainder is 67, so 70 is not a divisor of 5177)
5177 / 71 = 72.915492957746 (the remainder is 65, so 71 is not a divisor of 5177)