What are the divisors of 5392?

1, 2, 4, 8, 16, 337, 674, 1348, 2696, 5392

There is a total of 10 positive divisors.
The sum of these divisors is 10478.
The arithmetic mean is 1047.8.

8 even divisors

2, 4, 8, 16, 674, 1348, 2696, 5392

2 odd divisors

1, 337

How to compute the divisors of 5392?

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 5392 by each of the numbers from 1 to 5392 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)

5392 / 1 = 5392 (the remainder is 0, so 1 is a divisor of 5392)
5392 / 2 = 2696 (the remainder is 0, so 2 is a divisor of 5392)
5392 / 3 = 1797.3333333333 (the remainder is 1, so 3 is not a divisor of 5392)
...
5392 / 5391 = 1.0001854943424 (the remainder is 1, so 5391 is not a divisor of 5392)
5392 / 5392 = 1 (the remainder is 0, so 5392 is a divisor of 5392)

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 5392 (i.e. 73.430239002743). 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 $\frac{N}{d} = D$ )

5392 / 1 = 5392 (the remainder is 0, so 1 and 5392 are divisors of 5392)
5392 / 2 = 2696 (the remainder is 0, so 2 and 2696 are divisors of 5392)
5392 / 3 = 1797.3333333333 (the remainder is 1, so 3 is not a divisor of 5392)
...
5392 / 72 = 74.888888888889 (the remainder is 64, so 72 is not a divisor of 5392)
5392 / 73 = 73.86301369863 (the remainder is 63, so 73 is not a divisor of 5392)