What are the divisors of 5192?

1, 2, 4, 8, 11, 22, 44, 59, 88, 118, 236, 472, 649, 1298, 2596, 5192

There is a total of 16 positive divisors.
The sum of these divisors is 10800.
The arithmetic mean is 675.

12 even divisors

2, 4, 8, 22, 44, 88, 118, 236, 472, 1298, 2596, 5192

4 odd divisors

1, 11, 59, 649

How to compute the divisors of 5192?

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 5192 by each of the numbers from 1 to 5192 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)

5192 / 1 = 5192 (the remainder is 0, so 1 is a divisor of 5192)
5192 / 2 = 2596 (the remainder is 0, so 2 is a divisor of 5192)
5192 / 3 = 1730.6666666667 (the remainder is 2, so 3 is not a divisor of 5192)
...
5192 / 5191 = 1.0001926411096 (the remainder is 1, so 5191 is not a divisor of 5192)
5192 / 5192 = 1 (the remainder is 0, so 5192 is a divisor of 5192)

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 5192 (i.e. 72.055534138607). 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 $\frac{N}{d} = D$ )

5192 / 1 = 5192 (the remainder is 0, so 1 and 5192 are divisors of 5192)
5192 / 2 = 2596 (the remainder is 0, so 2 and 2596 are divisors of 5192)
5192 / 3 = 1730.6666666667 (the remainder is 2, so 3 is not a divisor of 5192)
...
5192 / 71 = 73.12676056338 (the remainder is 9, so 71 is not a divisor of 5192)
5192 / 72 = 72.111111111111 (the remainder is 8, so 72 is not a divisor of 5192)