What are the divisors of 2251?

1, 2251

There is a total of 2 positive divisors.
The sum of these divisors is 2252.
The arithmetic mean is 1126.

2 odd divisors

1, 2251

How to compute the divisors of 2251?

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 2251 by each of the numbers from 1 to 2251 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)

2251 / 1 = 2251 (the remainder is 0, so 1 is a divisor of 2251)
2251 / 2 = 1125.5 (the remainder is 1, so 2 is not a divisor of 2251)
2251 / 3 = 750.33333333333 (the remainder is 1, so 3 is not a divisor of 2251)
...
2251 / 2250 = 1.0004444444444 (the remainder is 1, so 2250 is not a divisor of 2251)
2251 / 2251 = 1 (the remainder is 0, so 2251 is a divisor of 2251)

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 2251 (i.e. 47.444704657106). 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 $\frac{N}{d} = D$ )

2251 / 1 = 2251 (the remainder is 0, so 1 and 2251 are divisors of 2251)
2251 / 2 = 1125.5 (the remainder is 1, so 2 is not a divisor of 2251)
2251 / 3 = 750.33333333333 (the remainder is 1, so 3 is not a divisor of 2251)
...
2251 / 46 = 48.934782608696 (the remainder is 43, so 46 is not a divisor of 2251)
2251 / 47 = 47.893617021277 (the remainder is 42, so 47 is not a divisor of 2251)