What are the divisors of 2258?

1, 2, 1129, 2258

There is a total of 4 positive divisors.
The sum of these divisors is 3390.
The arithmetic mean is 847.5.

2 even divisors

2, 2258

2 odd divisors

1, 1129

How to compute the divisors of 2258?

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 2258 by each of the numbers from 1 to 2258 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)

2258 / 1 = 2258 (the remainder is 0, so 1 is a divisor of 2258)
2258 / 2 = 1129 (the remainder is 0, so 2 is a divisor of 2258)
2258 / 3 = 752.66666666667 (the remainder is 2, so 3 is not a divisor of 2258)
...
2258 / 2257 = 1.0004430660168 (the remainder is 1, so 2257 is not a divisor of 2258)
2258 / 2258 = 1 (the remainder is 0, so 2258 is a divisor of 2258)

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 2258 (i.e. 47.518417482067). 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 $\frac{N}{d} = D$ )

2258 / 1 = 2258 (the remainder is 0, so 1 and 2258 are divisors of 2258)
2258 / 2 = 1129 (the remainder is 0, so 2 and 1129 are divisors of 2258)
2258 / 3 = 752.66666666667 (the remainder is 2, so 3 is not a divisor of 2258)
...
2258 / 46 = 49.086956521739 (the remainder is 4, so 46 is not a divisor of 2258)
2258 / 47 = 48.042553191489 (the remainder is 2, so 47 is not a divisor of 2258)