What are the divisors of 2445?

1, 3, 5, 15, 163, 489, 815, 2445

There is a total of 8 positive divisors.
The sum of these divisors is 3936.
The arithmetic mean is 492.

8 odd divisors

1, 3, 5, 15, 163, 489, 815, 2445

How to compute the divisors of 2445?

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 2445 by each of the numbers from 1 to 2445 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)

2445 / 1 = 2445 (the remainder is 0, so 1 is a divisor of 2445)
2445 / 2 = 1222.5 (the remainder is 1, so 2 is not a divisor of 2445)
2445 / 3 = 815 (the remainder is 0, so 3 is a divisor of 2445)
...
2445 / 2444 = 1.0004091653028 (the remainder is 1, so 2444 is not a divisor of 2445)
2445 / 2445 = 1 (the remainder is 0, so 2445 is a divisor of 2445)

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 2445 (i.e. 49.446941260304). 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 $\frac{N}{d} = D$ )

2445 / 1 = 2445 (the remainder is 0, so 1 and 2445 are divisors of 2445)
2445 / 2 = 1222.5 (the remainder is 1, so 2 is not a divisor of 2445)
2445 / 3 = 815 (the remainder is 0, so 3 and 815 are divisors of 2445)
...
2445 / 48 = 50.9375 (the remainder is 45, so 48 is not a divisor of 2445)
2445 / 49 = 49.897959183673 (the remainder is 44, so 49 is not a divisor of 2445)