What are the divisors of 2499?

1, 3, 7, 17, 21, 49, 51, 119, 147, 357, 833, 2499

There is a total of 12 positive divisors.
The sum of these divisors is 4104.
The arithmetic mean is 342.

12 odd divisors

1, 3, 7, 17, 21, 49, 51, 119, 147, 357, 833, 2499

How to compute the divisors of 2499?

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 2499 by each of the numbers from 1 to 2499 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)

2499 / 1 = 2499 (the remainder is 0, so 1 is a divisor of 2499)
2499 / 2 = 1249.5 (the remainder is 1, so 2 is not a divisor of 2499)
2499 / 3 = 833 (the remainder is 0, so 3 is a divisor of 2499)
...
2499 / 2498 = 1.0004003202562 (the remainder is 1, so 2498 is not a divisor of 2499)
2499 / 2499 = 1 (the remainder is 0, so 2499 is a divisor of 2499)

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 2499 (i.e. 49.9899989998). 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 $\frac{N}{d} = D$ )

2499 / 1 = 2499 (the remainder is 0, so 1 and 2499 are divisors of 2499)
2499 / 2 = 1249.5 (the remainder is 1, so 2 is not a divisor of 2499)
2499 / 3 = 833 (the remainder is 0, so 3 and 833 are divisors of 2499)
...
2499 / 48 = 52.0625 (the remainder is 3, so 48 is not a divisor of 2499)
2499 / 49 = 51 (the remainder is 0, so 49 and 51 are divisors of 2499)