What are the divisors of 2260?

1, 2, 4, 5, 10, 20, 113, 226, 452, 565, 1130, 2260

There is a total of 12 positive divisors.
The sum of these divisors is 4788.
The arithmetic mean is 399.

8 even divisors

2, 4, 10, 20, 226, 452, 1130, 2260

4 odd divisors

1, 5, 113, 565

How to compute the divisors of 2260?

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 2260 by each of the numbers from 1 to 2260 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)

2260 / 1 = 2260 (the remainder is 0, so 1 is a divisor of 2260)
2260 / 2 = 1130 (the remainder is 0, so 2 is a divisor of 2260)
2260 / 3 = 753.33333333333 (the remainder is 1, so 3 is not a divisor of 2260)
...
2260 / 2259 = 1.0004426737494 (the remainder is 1, so 2259 is not a divisor of 2260)
2260 / 2260 = 1 (the remainder is 0, so 2260 is a divisor of 2260)

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 2260 (i.e. 47.539457296019). 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 $\frac{N}{d} = D$ )

2260 / 1 = 2260 (the remainder is 0, so 1 and 2260 are divisors of 2260)
2260 / 2 = 1130 (the remainder is 0, so 2 and 1130 are divisors of 2260)
2260 / 3 = 753.33333333333 (the remainder is 1, so 3 is not a divisor of 2260)
...
2260 / 46 = 49.130434782609 (the remainder is 6, so 46 is not a divisor of 2260)
2260 / 47 = 48.085106382979 (the remainder is 4, so 47 is not a divisor of 2260)