What are the divisors of 5024?

1, 2, 4, 8, 16, 32, 157, 314, 628, 1256, 2512, 5024

There is a total of 12 positive divisors.
The sum of these divisors is 9954.
The arithmetic mean is 829.5.

10 even divisors

2, 4, 8, 16, 32, 314, 628, 1256, 2512, 5024

2 odd divisors

1, 157

How to compute the divisors of 5024?

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 5024 by each of the numbers from 1 to 5024 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)

5024 / 1 = 5024 (the remainder is 0, so 1 is a divisor of 5024)
5024 / 2 = 2512 (the remainder is 0, so 2 is a divisor of 5024)
5024 / 3 = 1674.6666666667 (the remainder is 2, so 3 is not a divisor of 5024)
...
5024 / 5023 = 1.0001990842126 (the remainder is 1, so 5023 is not a divisor of 5024)
5024 / 5024 = 1 (the remainder is 0, so 5024 is a divisor of 5024)

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 5024 (i.e. 70.880180586677). 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 $\frac{N}{d} = D$ )

5024 / 1 = 5024 (the remainder is 0, so 1 and 5024 are divisors of 5024)
5024 / 2 = 2512 (the remainder is 0, so 2 and 2512 are divisors of 5024)
5024 / 3 = 1674.6666666667 (the remainder is 2, so 3 is not a divisor of 5024)
...
5024 / 69 = 72.811594202899 (the remainder is 56, so 69 is not a divisor of 5024)
5024 / 70 = 71.771428571429 (the remainder is 54, so 70 is not a divisor of 5024)