What are the divisors of 2493?

1, 3, 9, 277, 831, 2493

There is a total of 6 positive divisors.
The sum of these divisors is 3614.
The arithmetic mean is 602.33333333333.

6 odd divisors

1, 3, 9, 277, 831, 2493

How to compute the divisors of 2493?

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 2493 by each of the numbers from 1 to 2493 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)

2493 / 1 = 2493 (the remainder is 0, so 1 is a divisor of 2493)
2493 / 2 = 1246.5 (the remainder is 1, so 2 is not a divisor of 2493)
2493 / 3 = 831 (the remainder is 0, so 3 is a divisor of 2493)
...
2493 / 2492 = 1.0004012841091 (the remainder is 1, so 2492 is not a divisor of 2493)
2493 / 2493 = 1 (the remainder is 0, so 2493 is a divisor of 2493)

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 2493 (i.e. 49.92995093128). 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 $\frac{N}{d} = D$ )

2493 / 1 = 2493 (the remainder is 0, so 1 and 2493 are divisors of 2493)
2493 / 2 = 1246.5 (the remainder is 1, so 2 is not a divisor of 2493)
2493 / 3 = 831 (the remainder is 0, so 3 and 831 are divisors of 2493)
...
2493 / 48 = 51.9375 (the remainder is 45, so 48 is not a divisor of 2493)
2493 / 49 = 50.877551020408 (the remainder is 43, so 49 is not a divisor of 2493)