What are the divisors of 2630?

1, 2, 5, 10, 263, 526, 1315, 2630

There is a total of 8 positive divisors.
The sum of these divisors is 4752.
The arithmetic mean is 594.

4 even divisors

2, 10, 526, 2630

4 odd divisors

1, 5, 263, 1315

How to compute the divisors of 2630?

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 2630 by each of the numbers from 1 to 2630 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)

2630 / 1 = 2630 (the remainder is 0, so 1 is a divisor of 2630)
2630 / 2 = 1315 (the remainder is 0, so 2 is a divisor of 2630)
2630 / 3 = 876.66666666667 (the remainder is 2, so 3 is not a divisor of 2630)
...
2630 / 2629 = 1.0003803727653 (the remainder is 1, so 2629 is not a divisor of 2630)
2630 / 2630 = 1 (the remainder is 0, so 2630 is a divisor of 2630)

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 2630 (i.e. 51.283525619832). 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 $\frac{N}{d} = D$ )

2630 / 1 = 2630 (the remainder is 0, so 1 and 2630 are divisors of 2630)
2630 / 2 = 1315 (the remainder is 0, so 2 and 1315 are divisors of 2630)
2630 / 3 = 876.66666666667 (the remainder is 2, so 3 is not a divisor of 2630)
...
2630 / 50 = 52.6 (the remainder is 30, so 50 is not a divisor of 2630)
2630 / 51 = 51.56862745098 (the remainder is 29, so 51 is not a divisor of 2630)