What are the divisors of 2248?

1, 2, 4, 8, 281, 562, 1124, 2248

There is a total of 8 positive divisors.
The sum of these divisors is 4230.
The arithmetic mean is 528.75.

6 even divisors

2, 4, 8, 562, 1124, 2248

2 odd divisors

1, 281

How to compute the divisors of 2248?

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 2248 by each of the numbers from 1 to 2248 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)

2248 / 1 = 2248 (the remainder is 0, so 1 is a divisor of 2248)
2248 / 2 = 1124 (the remainder is 0, so 2 is a divisor of 2248)
2248 / 3 = 749.33333333333 (the remainder is 1, so 3 is not a divisor of 2248)
...
2248 / 2247 = 1.0004450378282 (the remainder is 1, so 2247 is not a divisor of 2248)
2248 / 2248 = 1 (the remainder is 0, so 2248 is a divisor of 2248)

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 2248 (i.e. 47.413078364519). 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 $\frac{N}{d} = D$ )

2248 / 1 = 2248 (the remainder is 0, so 1 and 2248 are divisors of 2248)
2248 / 2 = 1124 (the remainder is 0, so 2 and 1124 are divisors of 2248)
2248 / 3 = 749.33333333333 (the remainder is 1, so 3 is not a divisor of 2248)
...
2248 / 46 = 48.869565217391 (the remainder is 40, so 46 is not a divisor of 2248)
2248 / 47 = 47.829787234043 (the remainder is 39, so 47 is not a divisor of 2248)