What are the divisors of 2254?

1, 2, 7, 14, 23, 46, 49, 98, 161, 322, 1127, 2254

There is a total of 12 positive divisors.
The sum of these divisors is 4104.
The arithmetic mean is 342.

6 even divisors

2, 14, 46, 98, 322, 2254

6 odd divisors

1, 7, 23, 49, 161, 1127

How to compute the divisors of 2254?

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 2254 by each of the numbers from 1 to 2254 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)

2254 / 1 = 2254 (the remainder is 0, so 1 is a divisor of 2254)
2254 / 2 = 1127 (the remainder is 0, so 2 is a divisor of 2254)
2254 / 3 = 751.33333333333 (the remainder is 1, so 3 is not a divisor of 2254)
...
2254 / 2253 = 1.0004438526409 (the remainder is 1, so 2253 is not a divisor of 2254)
2254 / 2254 = 1 (the remainder is 0, so 2254 is a divisor of 2254)

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 2254 (i.e. 47.476309881877). 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 $\frac{N}{d} = D$ )

2254 / 1 = 2254 (the remainder is 0, so 1 and 2254 are divisors of 2254)
2254 / 2 = 1127 (the remainder is 0, so 2 and 1127 are divisors of 2254)
2254 / 3 = 751.33333333333 (the remainder is 1, so 3 is not a divisor of 2254)
...
2254 / 46 = 49 (the remainder is 0, so 46 and 49 are divisors of 2254)
2254 / 47 = 47.957446808511 (the remainder is 45, so 47 is not a divisor of 2254)