What are the divisors of 2457?

1, 3, 7, 9, 13, 21, 27, 39, 63, 91, 117, 189, 273, 351, 819, 2457

There is a total of 16 positive divisors.
The sum of these divisors is 4480.
The arithmetic mean is 280.

16 odd divisors

1, 3, 7, 9, 13, 21, 27, 39, 63, 91, 117, 189, 273, 351, 819, 2457

How to compute the divisors of 2457?

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 2457 by each of the numbers from 1 to 2457 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)

2457 / 1 = 2457 (the remainder is 0, so 1 is a divisor of 2457)
2457 / 2 = 1228.5 (the remainder is 1, so 2 is not a divisor of 2457)
2457 / 3 = 819 (the remainder is 0, so 3 is a divisor of 2457)
...
2457 / 2456 = 1.0004071661238 (the remainder is 1, so 2456 is not a divisor of 2457)
2457 / 2457 = 1 (the remainder is 0, so 2457 is a divisor of 2457)

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 2457 (i.e. 49.568134925575). 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 $\frac{N}{d} = D$ )

2457 / 1 = 2457 (the remainder is 0, so 1 and 2457 are divisors of 2457)
2457 / 2 = 1228.5 (the remainder is 1, so 2 is not a divisor of 2457)
2457 / 3 = 819 (the remainder is 0, so 3 and 819 are divisors of 2457)
...
2457 / 48 = 51.1875 (the remainder is 9, so 48 is not a divisor of 2457)
2457 / 49 = 50.142857142857 (the remainder is 7, so 49 is not a divisor of 2457)