What are the divisors of 2264?

1, 2, 4, 8, 283, 566, 1132, 2264

There is a total of 8 positive divisors.
The sum of these divisors is 4260.
The arithmetic mean is 532.5.

6 even divisors

2, 4, 8, 566, 1132, 2264

2 odd divisors

1, 283

How to compute the divisors of 2264?

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 2264 by each of the numbers from 1 to 2264 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)

2264 / 1 = 2264 (the remainder is 0, so 1 is a divisor of 2264)
2264 / 2 = 1132 (the remainder is 0, so 2 is a divisor of 2264)
2264 / 3 = 754.66666666667 (the remainder is 2, so 3 is not a divisor of 2264)
...
2264 / 2263 = 1.0004418912947 (the remainder is 1, so 2263 is not a divisor of 2264)
2264 / 2264 = 1 (the remainder is 0, so 2264 is a divisor of 2264)

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 2264 (i.e. 47.581509013481). 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 $\frac{N}{d} = D$ )

2264 / 1 = 2264 (the remainder is 0, so 1 and 2264 are divisors of 2264)
2264 / 2 = 1132 (the remainder is 0, so 2 and 1132 are divisors of 2264)
2264 / 3 = 754.66666666667 (the remainder is 2, so 3 is not a divisor of 2264)
...
2264 / 46 = 49.217391304348 (the remainder is 10, so 46 is not a divisor of 2264)
2264 / 47 = 48.170212765957 (the remainder is 8, so 47 is not a divisor of 2264)