What are the divisors of 5231?

1, 5231

There is a total of 2 positive divisors.
The sum of these divisors is 5232.
The arithmetic mean is 2616.

2 odd divisors

1, 5231

How to compute the divisors of 5231?

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 5231 by each of the numbers from 1 to 5231 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)

5231 / 1 = 5231 (the remainder is 0, so 1 is a divisor of 5231)
5231 / 2 = 2615.5 (the remainder is 1, so 2 is not a divisor of 5231)
5231 / 3 = 1743.6666666667 (the remainder is 2, so 3 is not a divisor of 5231)
...
5231 / 5230 = 1.0001912045889 (the remainder is 1, so 5230 is not a divisor of 5231)
5231 / 5231 = 1 (the remainder is 0, so 5231 is a divisor of 5231)

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 5231 (i.e. 72.325652433974). 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 $\frac{N}{d} = D$ )

5231 / 1 = 5231 (the remainder is 0, so 1 and 5231 are divisors of 5231)
5231 / 2 = 2615.5 (the remainder is 1, so 2 is not a divisor of 5231)
5231 / 3 = 1743.6666666667 (the remainder is 2, so 3 is not a divisor of 5231)
...
5231 / 71 = 73.676056338028 (the remainder is 48, so 71 is not a divisor of 5231)
5231 / 72 = 72.652777777778 (the remainder is 47, so 72 is not a divisor of 5231)