What are the divisors of 2275?

1, 5, 7, 13, 25, 35, 65, 91, 175, 325, 455, 2275

There is a total of 12 positive divisors.
The sum of these divisors is 3472.
The arithmetic mean is 289.33333333333.

12 odd divisors

1, 5, 7, 13, 25, 35, 65, 91, 175, 325, 455, 2275

How to compute the divisors of 2275?

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 2275 by each of the numbers from 1 to 2275 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)

2275 / 1 = 2275 (the remainder is 0, so 1 is a divisor of 2275)
2275 / 2 = 1137.5 (the remainder is 1, so 2 is not a divisor of 2275)
2275 / 3 = 758.33333333333 (the remainder is 1, so 3 is not a divisor of 2275)
...
2275 / 2274 = 1.0004397537379 (the remainder is 1, so 2274 is not a divisor of 2275)
2275 / 2275 = 1 (the remainder is 0, so 2275 is a divisor of 2275)

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 2275 (i.e. 47.696960070847). 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 $\frac{N}{d} = D$ )

2275 / 1 = 2275 (the remainder is 0, so 1 and 2275 are divisors of 2275)
2275 / 2 = 1137.5 (the remainder is 1, so 2 is not a divisor of 2275)
2275 / 3 = 758.33333333333 (the remainder is 1, so 3 is not a divisor of 2275)
...
2275 / 46 = 49.45652173913 (the remainder is 21, so 46 is not a divisor of 2275)
2275 / 47 = 48.404255319149 (the remainder is 19, so 47 is not a divisor of 2275)