What are the divisors of 5422?

1, 2, 2711, 5422

There is a total of 4 positive divisors.
The sum of these divisors is 8136.
The arithmetic mean is 2034.

2 even divisors

2, 5422

2 odd divisors

1, 2711

How to compute the divisors of 5422?

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 5422 by each of the numbers from 1 to 5422 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)

5422 / 1 = 5422 (the remainder is 0, so 1 is a divisor of 5422)
5422 / 2 = 2711 (the remainder is 0, so 2 is a divisor of 5422)
5422 / 3 = 1807.3333333333 (the remainder is 1, so 3 is not a divisor of 5422)
...
5422 / 5421 = 1.0001844678104 (the remainder is 1, so 5421 is not a divisor of 5422)
5422 / 5422 = 1 (the remainder is 0, so 5422 is a divisor of 5422)

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 5422 (i.e. 73.63423117002). 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 $\frac{N}{d} = D$ )

5422 / 1 = 5422 (the remainder is 0, so 1 and 5422 are divisors of 5422)
5422 / 2 = 2711 (the remainder is 0, so 2 and 2711 are divisors of 5422)
5422 / 3 = 1807.3333333333 (the remainder is 1, so 3 is not a divisor of 5422)
...
5422 / 72 = 75.305555555556 (the remainder is 22, so 72 is not a divisor of 5422)
5422 / 73 = 74.27397260274 (the remainder is 20, so 73 is not a divisor of 5422)