What are the divisors of 5237?

1, 5237

There is a total of 2 positive divisors.
The sum of these divisors is 5238.
The arithmetic mean is 2619.

2 odd divisors

1, 5237

How to compute the divisors of 5237?

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 5237 by each of the numbers from 1 to 5237 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)

5237 / 1 = 5237 (the remainder is 0, so 1 is a divisor of 5237)
5237 / 2 = 2618.5 (the remainder is 1, so 2 is not a divisor of 5237)
5237 / 3 = 1745.6666666667 (the remainder is 2, so 3 is not a divisor of 5237)
...
5237 / 5236 = 1.0001909854851 (the remainder is 1, so 5236 is not a divisor of 5237)
5237 / 5237 = 1 (the remainder is 0, so 5237 is a divisor of 5237)

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 5237 (i.e. 72.367119605523). 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 $\frac{N}{d} = D$ )

5237 / 1 = 5237 (the remainder is 0, so 1 and 5237 are divisors of 5237)
5237 / 2 = 2618.5 (the remainder is 1, so 2 is not a divisor of 5237)
5237 / 3 = 1745.6666666667 (the remainder is 2, so 3 is not a divisor of 5237)
...
5237 / 71 = 73.760563380282 (the remainder is 54, so 71 is not a divisor of 5237)
5237 / 72 = 72.736111111111 (the remainder is 53, so 72 is not a divisor of 5237)