What are the divisors of 2274?

1, 2, 3, 6, 379, 758, 1137, 2274

There is a total of 8 positive divisors.
The sum of these divisors is 4560.
The arithmetic mean is 570.

4 even divisors

2, 6, 758, 2274

4 odd divisors

1, 3, 379, 1137

How to compute the divisors of 2274?

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 2274 by each of the numbers from 1 to 2274 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)

2274 / 1 = 2274 (the remainder is 0, so 1 is a divisor of 2274)
2274 / 2 = 1137 (the remainder is 0, so 2 is a divisor of 2274)
2274 / 3 = 758 (the remainder is 0, so 3 is a divisor of 2274)
...
2274 / 2273 = 1.0004399472063 (the remainder is 1, so 2273 is not a divisor of 2274)
2274 / 2274 = 1 (the remainder is 0, so 2274 is a divisor of 2274)

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 2274 (i.e. 47.686476070265). 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 $\frac{N}{d} = D$ )

2274 / 1 = 2274 (the remainder is 0, so 1 and 2274 are divisors of 2274)
2274 / 2 = 1137 (the remainder is 0, so 2 and 1137 are divisors of 2274)
2274 / 3 = 758 (the remainder is 0, so 3 and 758 are divisors of 2274)
...
2274 / 46 = 49.434782608696 (the remainder is 20, so 46 is not a divisor of 2274)
2274 / 47 = 48.382978723404 (the remainder is 18, so 47 is not a divisor of 2274)