What are the divisors of 5296?

1, 2, 4, 8, 16, 331, 662, 1324, 2648, 5296

There is a total of 10 positive divisors.
The sum of these divisors is 10292.
The arithmetic mean is 1029.2.

8 even divisors

2, 4, 8, 16, 662, 1324, 2648, 5296

2 odd divisors

1, 331

How to compute the divisors of 5296?

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 5296 by each of the numbers from 1 to 5296 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)

5296 / 1 = 5296 (the remainder is 0, so 1 is a divisor of 5296)
5296 / 2 = 2648 (the remainder is 0, so 2 is a divisor of 5296)
5296 / 3 = 1765.3333333333 (the remainder is 1, so 3 is not a divisor of 5296)
...
5296 / 5295 = 1.0001888574127 (the remainder is 1, so 5295 is not a divisor of 5296)
5296 / 5296 = 1 (the remainder is 0, so 5296 is a divisor of 5296)

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 5296 (i.e. 72.773621594641). 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 $\frac{N}{d} = D$ )

5296 / 1 = 5296 (the remainder is 0, so 1 and 5296 are divisors of 5296)
5296 / 2 = 2648 (the remainder is 0, so 2 and 2648 are divisors of 5296)
5296 / 3 = 1765.3333333333 (the remainder is 1, so 3 is not a divisor of 5296)
...
5296 / 71 = 74.591549295775 (the remainder is 42, so 71 is not a divisor of 5296)
5296 / 72 = 73.555555555556 (the remainder is 40, so 72 is not a divisor of 5296)