What are the divisors of 2622?

1, 2, 3, 6, 19, 23, 38, 46, 57, 69, 114, 138, 437, 874, 1311, 2622

There is a total of 16 positive divisors.
The sum of these divisors is 5760.
The arithmetic mean is 360.

8 even divisors

2, 6, 38, 46, 114, 138, 874, 2622

8 odd divisors

1, 3, 19, 23, 57, 69, 437, 1311

How to compute the divisors of 2622?

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 2622 by each of the numbers from 1 to 2622 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)

2622 / 1 = 2622 (the remainder is 0, so 1 is a divisor of 2622)
2622 / 2 = 1311 (the remainder is 0, so 2 is a divisor of 2622)
2622 / 3 = 874 (the remainder is 0, so 3 is a divisor of 2622)
...
2622 / 2621 = 1.0003815337657 (the remainder is 1, so 2621 is not a divisor of 2622)
2622 / 2622 = 1 (the remainder is 0, so 2622 is a divisor of 2622)

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 2622 (i.e. 51.205468457968). 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 $\frac{N}{d} = D$ )

2622 / 1 = 2622 (the remainder is 0, so 1 and 2622 are divisors of 2622)
2622 / 2 = 1311 (the remainder is 0, so 2 and 1311 are divisors of 2622)
2622 / 3 = 874 (the remainder is 0, so 3 and 874 are divisors of 2622)
...
2622 / 50 = 52.44 (the remainder is 22, so 50 is not a divisor of 2622)
2622 / 51 = 51.411764705882 (the remainder is 21, so 51 is not a divisor of 2622)