What are the divisors of 5264?

1, 2, 4, 7, 8, 14, 16, 28, 47, 56, 94, 112, 188, 329, 376, 658, 752, 1316, 2632, 5264

There is a total of 20 positive divisors.
The sum of these divisors is 11904.
The arithmetic mean is 595.2.

16 even divisors

2, 4, 8, 14, 16, 28, 56, 94, 112, 188, 376, 658, 752, 1316, 2632, 5264

4 odd divisors

1, 7, 47, 329

How to compute the divisors of 5264?

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 5264 by each of the numbers from 1 to 5264 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)

5264 / 1 = 5264 (the remainder is 0, so 1 is a divisor of 5264)
5264 / 2 = 2632 (the remainder is 0, so 2 is a divisor of 5264)
5264 / 3 = 1754.6666666667 (the remainder is 2, so 3 is not a divisor of 5264)
...
5264 / 5263 = 1.0001900057002 (the remainder is 1, so 5263 is not a divisor of 5264)
5264 / 5264 = 1 (the remainder is 0, so 5264 is a divisor of 5264)

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 5264 (i.e. 72.553428588868). 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 $\frac{N}{d} = D$ )

5264 / 1 = 5264 (the remainder is 0, so 1 and 5264 are divisors of 5264)
5264 / 2 = 2632 (the remainder is 0, so 2 and 2632 are divisors of 5264)
5264 / 3 = 1754.6666666667 (the remainder is 2, so 3 is not a divisor of 5264)
...
5264 / 71 = 74.140845070423 (the remainder is 10, so 71 is not a divisor of 5264)
5264 / 72 = 73.111111111111 (the remainder is 8, so 72 is not a divisor of 5264)