What are the divisors of 2540?

1, 2, 4, 5, 10, 20, 127, 254, 508, 635, 1270, 2540

There is a total of 12 positive divisors.
The sum of these divisors is 5376.
The arithmetic mean is 448.

8 even divisors

2, 4, 10, 20, 254, 508, 1270, 2540

4 odd divisors

1, 5, 127, 635

How to compute the divisors of 2540?

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 2540 by each of the numbers from 1 to 2540 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)

2540 / 1 = 2540 (the remainder is 0, so 1 is a divisor of 2540)
2540 / 2 = 1270 (the remainder is 0, so 2 is a divisor of 2540)
2540 / 3 = 846.66666666667 (the remainder is 2, so 3 is not a divisor of 2540)
...
2540 / 2539 = 1.0003938558488 (the remainder is 1, so 2539 is not a divisor of 2540)
2540 / 2540 = 1 (the remainder is 0, so 2540 is a divisor of 2540)

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 2540 (i.e. 50.398412673417). 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 $\frac{N}{d} = D$ )

2540 / 1 = 2540 (the remainder is 0, so 1 and 2540 are divisors of 2540)
2540 / 2 = 1270 (the remainder is 0, so 2 and 1270 are divisors of 2540)
2540 / 3 = 846.66666666667 (the remainder is 2, so 3 is not a divisor of 2540)
...
2540 / 49 = 51.836734693878 (the remainder is 41, so 49 is not a divisor of 2540)
2540 / 50 = 50.8 (the remainder is 40, so 50 is not a divisor of 2540)