What are the divisors of 5216?

1, 2, 4, 8, 16, 32, 163, 326, 652, 1304, 2608, 5216

There is a total of 12 positive divisors.
The sum of these divisors is 10332.
The arithmetic mean is 861.

10 even divisors

2, 4, 8, 16, 32, 326, 652, 1304, 2608, 5216

2 odd divisors

1, 163

How to compute the divisors of 5216?

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 5216 by each of the numbers from 1 to 5216 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)

5216 / 1 = 5216 (the remainder is 0, so 1 is a divisor of 5216)
5216 / 2 = 2608 (the remainder is 0, so 2 is a divisor of 5216)
5216 / 3 = 1738.6666666667 (the remainder is 2, so 3 is not a divisor of 5216)
...
5216 / 5215 = 1.0001917545542 (the remainder is 1, so 5215 is not a divisor of 5216)
5216 / 5216 = 1 (the remainder is 0, so 5216 is a divisor of 5216)

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 5216 (i.e. 72.221880341071). 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 $\frac{N}{d} = D$ )

5216 / 1 = 5216 (the remainder is 0, so 1 and 5216 are divisors of 5216)
5216 / 2 = 2608 (the remainder is 0, so 2 and 2608 are divisors of 5216)
5216 / 3 = 1738.6666666667 (the remainder is 2, so 3 is not a divisor of 5216)
...
5216 / 71 = 73.464788732394 (the remainder is 33, so 71 is not a divisor of 5216)
5216 / 72 = 72.444444444444 (the remainder is 32, so 72 is not a divisor of 5216)