What are the divisors of 5492?

1, 2, 4, 1373, 2746, 5492

There is a total of 6 positive divisors.
The sum of these divisors is 9618.
The arithmetic mean is 1603.

4 even divisors

2, 4, 2746, 5492

2 odd divisors

1, 1373

How to compute the divisors of 5492?

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 5492 by each of the numbers from 1 to 5492 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)

5492 / 1 = 5492 (the remainder is 0, so 1 is a divisor of 5492)
5492 / 2 = 2746 (the remainder is 0, so 2 is a divisor of 5492)
5492 / 3 = 1830.6666666667 (the remainder is 2, so 3 is not a divisor of 5492)
...
5492 / 5491 = 1.0001821161901 (the remainder is 1, so 5491 is not a divisor of 5492)
5492 / 5492 = 1 (the remainder is 0, so 5492 is a divisor of 5492)

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 5492 (i.e. 74.108029254596). 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 $\frac{N}{d} = D$ )

5492 / 1 = 5492 (the remainder is 0, so 1 and 5492 are divisors of 5492)
5492 / 2 = 2746 (the remainder is 0, so 2 and 2746 are divisors of 5492)
5492 / 3 = 1830.6666666667 (the remainder is 2, so 3 is not a divisor of 5492)
...
5492 / 73 = 75.232876712329 (the remainder is 17, so 73 is not a divisor of 5492)
5492 / 74 = 74.216216216216 (the remainder is 16, so 74 is not a divisor of 5492)