What are the divisors of 2250?

1, 2, 3, 5, 6, 9, 10, 15, 18, 25, 30, 45, 50, 75, 90, 125, 150, 225, 250, 375, 450, 750, 1125, 2250

There is a total of 24 positive divisors.
The sum of these divisors is 6084.
The arithmetic mean is 253.5.

12 even divisors

2, 6, 10, 18, 30, 50, 90, 150, 250, 450, 750, 2250

12 odd divisors

1, 3, 5, 9, 15, 25, 45, 75, 125, 225, 375, 1125

How to compute the divisors of 2250?

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 2250 by each of the numbers from 1 to 2250 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)

2250 / 1 = 2250 (the remainder is 0, so 1 is a divisor of 2250)
2250 / 2 = 1125 (the remainder is 0, so 2 is a divisor of 2250)
2250 / 3 = 750 (the remainder is 0, so 3 is a divisor of 2250)
...
2250 / 2249 = 1.0004446420631 (the remainder is 1, so 2249 is not a divisor of 2250)
2250 / 2250 = 1 (the remainder is 0, so 2250 is a divisor of 2250)

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 2250 (i.e. 47.434164902526). 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 $\frac{N}{d} = D$ )

2250 / 1 = 2250 (the remainder is 0, so 1 and 2250 are divisors of 2250)
2250 / 2 = 1125 (the remainder is 0, so 2 and 1125 are divisors of 2250)
2250 / 3 = 750 (the remainder is 0, so 3 and 750 are divisors of 2250)
...
2250 / 46 = 48.913043478261 (the remainder is 42, so 46 is not a divisor of 2250)
2250 / 47 = 47.872340425532 (the remainder is 41, so 47 is not a divisor of 2250)