What are the divisors of 2276?

1, 2, 4, 569, 1138, 2276

There is a total of 6 positive divisors.
The sum of these divisors is 3990.
The arithmetic mean is 665.

4 even divisors

2, 4, 1138, 2276

2 odd divisors

1, 569

How to compute the divisors of 2276?

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 2276 by each of the numbers from 1 to 2276 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)

2276 / 1 = 2276 (the remainder is 0, so 1 is a divisor of 2276)
2276 / 2 = 1138 (the remainder is 0, so 2 is a divisor of 2276)
2276 / 3 = 758.66666666667 (the remainder is 2, so 3 is not a divisor of 2276)
...
2276 / 2275 = 1.0004395604396 (the remainder is 1, so 2275 is not a divisor of 2276)
2276 / 2276 = 1 (the remainder is 0, so 2276 is a divisor of 2276)

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 2276 (i.e. 47.707441767506). 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 $\frac{N}{d} = D$ )

2276 / 1 = 2276 (the remainder is 0, so 1 and 2276 are divisors of 2276)
2276 / 2 = 1138 (the remainder is 0, so 2 and 1138 are divisors of 2276)
2276 / 3 = 758.66666666667 (the remainder is 2, so 3 is not a divisor of 2276)
...
2276 / 46 = 49.478260869565 (the remainder is 22, so 46 is not a divisor of 2276)
2276 / 47 = 48.425531914894 (the remainder is 20, so 47 is not a divisor of 2276)