What are the divisors of 5248?

1, 2, 4, 8, 16, 32, 41, 64, 82, 128, 164, 328, 656, 1312, 2624, 5248

There is a total of 16 positive divisors.
The sum of these divisors is 10710.
The arithmetic mean is 669.375.

14 even divisors

2, 4, 8, 16, 32, 64, 82, 128, 164, 328, 656, 1312, 2624, 5248

2 odd divisors

1, 41

How to compute the divisors of 5248?

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 5248 by each of the numbers from 1 to 5248 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)

5248 / 1 = 5248 (the remainder is 0, so 1 is a divisor of 5248)
5248 / 2 = 2624 (the remainder is 0, so 2 is a divisor of 5248)
5248 / 3 = 1749.3333333333 (the remainder is 1, so 3 is not a divisor of 5248)
...
5248 / 5247 = 1.0001905850962 (the remainder is 1, so 5247 is not a divisor of 5248)
5248 / 5248 = 1 (the remainder is 0, so 5248 is a divisor of 5248)

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 5248 (i.e. 72.443081105099). 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 $\frac{N}{d} = D$ )

5248 / 1 = 5248 (the remainder is 0, so 1 and 5248 are divisors of 5248)
5248 / 2 = 2624 (the remainder is 0, so 2 and 2624 are divisors of 5248)
5248 / 3 = 1749.3333333333 (the remainder is 1, so 3 is not a divisor of 5248)
...
5248 / 71 = 73.915492957746 (the remainder is 65, so 71 is not a divisor of 5248)
5248 / 72 = 72.888888888889 (the remainder is 64, so 72 is not a divisor of 5248)