What are the divisors of 2257?

1, 37, 61, 2257

There is a total of 4 positive divisors.
The sum of these divisors is 2356.
The arithmetic mean is 589.

4 odd divisors

1, 37, 61, 2257

How to compute the divisors of 2257?

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 2257 by each of the numbers from 1 to 2257 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)

2257 / 1 = 2257 (the remainder is 0, so 1 is a divisor of 2257)
2257 / 2 = 1128.5 (the remainder is 1, so 2 is not a divisor of 2257)
2257 / 3 = 752.33333333333 (the remainder is 1, so 3 is not a divisor of 2257)
...
2257 / 2256 = 1.0004432624113 (the remainder is 1, so 2256 is not a divisor of 2257)
2257 / 2257 = 1 (the remainder is 0, so 2257 is a divisor of 2257)

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 2257 (i.e. 47.507894080879). 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 $\frac{N}{d} = D$ )

2257 / 1 = 2257 (the remainder is 0, so 1 and 2257 are divisors of 2257)
2257 / 2 = 1128.5 (the remainder is 1, so 2 is not a divisor of 2257)
2257 / 3 = 752.33333333333 (the remainder is 1, so 3 is not a divisor of 2257)
...
2257 / 46 = 49.065217391304 (the remainder is 3, so 46 is not a divisor of 2257)
2257 / 47 = 48.021276595745 (the remainder is 1, so 47 is not a divisor of 2257)