What are the divisors of 2235?

1, 3, 5, 15, 149, 447, 745, 2235

There is a total of 8 positive divisors.
The sum of these divisors is 3600.
The arithmetic mean is 450.

8 odd divisors

1, 3, 5, 15, 149, 447, 745, 2235

How to compute the divisors of 2235?

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 2235 by each of the numbers from 1 to 2235 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)

2235 / 1 = 2235 (the remainder is 0, so 1 is a divisor of 2235)
2235 / 2 = 1117.5 (the remainder is 1, so 2 is not a divisor of 2235)
2235 / 3 = 745 (the remainder is 0, so 3 is a divisor of 2235)
...
2235 / 2234 = 1.0004476275739 (the remainder is 1, so 2234 is not a divisor of 2235)
2235 / 2235 = 1 (the remainder is 0, so 2235 is a divisor of 2235)

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 2235 (i.e. 47.275786614291). 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 $\frac{N}{d} = D$ )

2235 / 1 = 2235 (the remainder is 0, so 1 and 2235 are divisors of 2235)
2235 / 2 = 1117.5 (the remainder is 1, so 2 is not a divisor of 2235)
2235 / 3 = 745 (the remainder is 0, so 3 and 745 are divisors of 2235)
...
2235 / 46 = 48.586956521739 (the remainder is 27, so 46 is not a divisor of 2235)
2235 / 47 = 47.553191489362 (the remainder is 26, so 47 is not a divisor of 2235)