What are the divisors of 5092?

1, 2, 4, 19, 38, 67, 76, 134, 268, 1273, 2546, 5092

There is a total of 12 positive divisors.
The sum of these divisors is 9520.
The arithmetic mean is 793.33333333333.

8 even divisors

2, 4, 38, 76, 134, 268, 2546, 5092

4 odd divisors

1, 19, 67, 1273

How to compute the divisors of 5092?

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 5092 by each of the numbers from 1 to 5092 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)

5092 / 1 = 5092 (the remainder is 0, so 1 is a divisor of 5092)
5092 / 2 = 2546 (the remainder is 0, so 2 is a divisor of 5092)
5092 / 3 = 1697.3333333333 (the remainder is 1, so 3 is not a divisor of 5092)
...
5092 / 5091 = 1.0001964250638 (the remainder is 1, so 5091 is not a divisor of 5092)
5092 / 5092 = 1 (the remainder is 0, so 5092 is a divisor of 5092)

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 5092 (i.e. 71.358251099645). 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 $\frac{N}{d} = D$ )

5092 / 1 = 5092 (the remainder is 0, so 1 and 5092 are divisors of 5092)
5092 / 2 = 2546 (the remainder is 0, so 2 and 2546 are divisors of 5092)
5092 / 3 = 1697.3333333333 (the remainder is 1, so 3 is not a divisor of 5092)
...
5092 / 70 = 72.742857142857 (the remainder is 52, so 70 is not a divisor of 5092)
5092 / 71 = 71.718309859155 (the remainder is 51, so 71 is not a divisor of 5092)