What are the divisors of 2252?

1, 2, 4, 563, 1126, 2252

There is a total of 6 positive divisors.
The sum of these divisors is 3948.
The arithmetic mean is 658.

4 even divisors

2, 4, 1126, 2252

2 odd divisors

1, 563

How to compute the divisors of 2252?

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 2252 by each of the numbers from 1 to 2252 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)

2252 / 1 = 2252 (the remainder is 0, so 1 is a divisor of 2252)
2252 / 2 = 1126 (the remainder is 0, so 2 is a divisor of 2252)
2252 / 3 = 750.66666666667 (the remainder is 2, so 3 is not a divisor of 2252)
...
2252 / 2251 = 1.0004442470013 (the remainder is 1, so 2251 is not a divisor of 2252)
2252 / 2252 = 1 (the remainder is 0, so 2252 is a divisor of 2252)

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 2252 (i.e. 47.455242070819). 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 $\frac{N}{d} = D$ )

2252 / 1 = 2252 (the remainder is 0, so 1 and 2252 are divisors of 2252)
2252 / 2 = 1126 (the remainder is 0, so 2 and 1126 are divisors of 2252)
2252 / 3 = 750.66666666667 (the remainder is 2, so 3 is not a divisor of 2252)
...
2252 / 46 = 48.95652173913 (the remainder is 44, so 46 is not a divisor of 2252)
2252 / 47 = 47.914893617021 (the remainder is 43, so 47 is not a divisor of 2252)