What are the divisors of 2634?

1, 2, 3, 6, 439, 878, 1317, 2634

There is a total of 8 positive divisors.
The sum of these divisors is 5280.
The arithmetic mean is 660.

4 even divisors

2, 6, 878, 2634

4 odd divisors

1, 3, 439, 1317

How to compute the divisors of 2634?

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 2634 by each of the numbers from 1 to 2634 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)

2634 / 1 = 2634 (the remainder is 0, so 1 is a divisor of 2634)
2634 / 2 = 1317 (the remainder is 0, so 2 is a divisor of 2634)
2634 / 3 = 878 (the remainder is 0, so 3 is a divisor of 2634)
...
2634 / 2633 = 1.0003797949107 (the remainder is 1, so 2633 is not a divisor of 2634)
2634 / 2634 = 1 (the remainder is 0, so 2634 is a divisor of 2634)

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 2634 (i.e. 51.322509681425). 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 $\frac{N}{d} = D$ )

2634 / 1 = 2634 (the remainder is 0, so 1 and 2634 are divisors of 2634)
2634 / 2 = 1317 (the remainder is 0, so 2 and 1317 are divisors of 2634)
2634 / 3 = 878 (the remainder is 0, so 3 and 878 are divisors of 2634)
...
2634 / 50 = 52.68 (the remainder is 34, so 50 is not a divisor of 2634)
2634 / 51 = 51.647058823529 (the remainder is 33, so 51 is not a divisor of 2634)