What are the divisors of 2253?

1, 3, 751, 2253

There is a total of 4 positive divisors.
The sum of these divisors is 3008.
The arithmetic mean is 752.

4 odd divisors

1, 3, 751, 2253

How to compute the divisors of 2253?

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 2253 by each of the numbers from 1 to 2253 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)

2253 / 1 = 2253 (the remainder is 0, so 1 is a divisor of 2253)
2253 / 2 = 1126.5 (the remainder is 1, so 2 is not a divisor of 2253)
2253 / 3 = 751 (the remainder is 0, so 3 is a divisor of 2253)
...
2253 / 2252 = 1.0004440497336 (the remainder is 1, so 2252 is not a divisor of 2253)
2253 / 2253 = 1 (the remainder is 0, so 2253 is a divisor of 2253)

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 2253 (i.e. 47.465777145223). 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 $\frac{N}{d} = D$ )

2253 / 1 = 2253 (the remainder is 0, so 1 and 2253 are divisors of 2253)
2253 / 2 = 1126.5 (the remainder is 1, so 2 is not a divisor of 2253)
2253 / 3 = 751 (the remainder is 0, so 3 and 751 are divisors of 2253)
...
2253 / 46 = 48.978260869565 (the remainder is 45, so 46 is not a divisor of 2253)
2253 / 47 = 47.936170212766 (the remainder is 44, so 47 is not a divisor of 2253)