What are the divisors of 2650?

1, 2, 5, 10, 25, 50, 53, 106, 265, 530, 1325, 2650

There is a total of 12 positive divisors.
The sum of these divisors is 5022.
The arithmetic mean is 418.5.

6 even divisors

2, 10, 50, 106, 530, 2650

6 odd divisors

1, 5, 25, 53, 265, 1325

How to compute the divisors of 2650?

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 2650 by each of the numbers from 1 to 2650 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)

2650 / 1 = 2650 (the remainder is 0, so 1 is a divisor of 2650)
2650 / 2 = 1325 (the remainder is 0, so 2 is a divisor of 2650)
2650 / 3 = 883.33333333333 (the remainder is 1, so 3 is not a divisor of 2650)
...
2650 / 2649 = 1.0003775009438 (the remainder is 1, so 2649 is not a divisor of 2650)
2650 / 2650 = 1 (the remainder is 0, so 2650 is a divisor of 2650)

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 2650 (i.e. 51.478150704935). 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 $\frac{N}{d} = D$ )

2650 / 1 = 2650 (the remainder is 0, so 1 and 2650 are divisors of 2650)
2650 / 2 = 1325 (the remainder is 0, so 2 and 1325 are divisors of 2650)
2650 / 3 = 883.33333333333 (the remainder is 1, so 3 is not a divisor of 2650)
...
2650 / 50 = 53 (the remainder is 0, so 50 and 53 are divisors of 2650)
2650 / 51 = 51.960784313725 (the remainder is 49, so 51 is not a divisor of 2650)