What are the divisors of 5056?

1, 2, 4, 8, 16, 32, 64, 79, 158, 316, 632, 1264, 2528, 5056

There is a total of 14 positive divisors.
The sum of these divisors is 10160.
The arithmetic mean is 725.71428571429.

12 even divisors

2, 4, 8, 16, 32, 64, 158, 316, 632, 1264, 2528, 5056

2 odd divisors

1, 79

How to compute the divisors of 5056?

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 5056 by each of the numbers from 1 to 5056 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)

5056 / 1 = 5056 (the remainder is 0, so 1 is a divisor of 5056)
5056 / 2 = 2528 (the remainder is 0, so 2 is a divisor of 5056)
5056 / 3 = 1685.3333333333 (the remainder is 1, so 3 is not a divisor of 5056)
...
5056 / 5055 = 1.0001978239367 (the remainder is 1, so 5055 is not a divisor of 5056)
5056 / 5056 = 1 (the remainder is 0, so 5056 is a divisor of 5056)

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 5056 (i.e. 71.105555338525). 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 $\frac{N}{d} = D$ )

5056 / 1 = 5056 (the remainder is 0, so 1 and 5056 are divisors of 5056)
5056 / 2 = 2528 (the remainder is 0, so 2 and 2528 are divisors of 5056)
5056 / 3 = 1685.3333333333 (the remainder is 1, so 3 is not a divisor of 5056)
...
5056 / 70 = 72.228571428571 (the remainder is 16, so 70 is not a divisor of 5056)
5056 / 71 = 71.211267605634 (the remainder is 15, so 71 is not a divisor of 5056)