What are the divisors of 2245?

1, 5, 449, 2245

There is a total of 4 positive divisors.
The sum of these divisors is 2700.
The arithmetic mean is 675.

4 odd divisors

1, 5, 449, 2245

How to compute the divisors of 2245?

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 2245 by each of the numbers from 1 to 2245 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)

2245 / 1 = 2245 (the remainder is 0, so 1 is a divisor of 2245)
2245 / 2 = 1122.5 (the remainder is 1, so 2 is not a divisor of 2245)
2245 / 3 = 748.33333333333 (the remainder is 1, so 3 is not a divisor of 2245)
...
2245 / 2244 = 1.0004456327986 (the remainder is 1, so 2244 is not a divisor of 2245)
2245 / 2245 = 1 (the remainder is 0, so 2245 is a divisor of 2245)

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 2245 (i.e. 47.381430961929). 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 $\frac{N}{d} = D$ )

2245 / 1 = 2245 (the remainder is 0, so 1 and 2245 are divisors of 2245)
2245 / 2 = 1122.5 (the remainder is 1, so 2 is not a divisor of 2245)
2245 / 3 = 748.33333333333 (the remainder is 1, so 3 is not a divisor of 2245)
...
2245 / 46 = 48.804347826087 (the remainder is 37, so 46 is not a divisor of 2245)
2245 / 47 = 47.765957446809 (the remainder is 36, so 47 is not a divisor of 2245)