What are the divisors of 2494?

1, 2, 29, 43, 58, 86, 1247, 2494

There is a total of 8 positive divisors.
The sum of these divisors is 3960.
The arithmetic mean is 495.

4 even divisors

2, 58, 86, 2494

4 odd divisors

1, 29, 43, 1247

How to compute the divisors of 2494?

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 2494 by each of the numbers from 1 to 2494 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)

2494 / 1 = 2494 (the remainder is 0, so 1 is a divisor of 2494)
2494 / 2 = 1247 (the remainder is 0, so 2 is a divisor of 2494)
2494 / 3 = 831.33333333333 (the remainder is 1, so 3 is not a divisor of 2494)
...
2494 / 2493 = 1.0004011231448 (the remainder is 1, so 2493 is not a divisor of 2494)
2494 / 2494 = 1 (the remainder is 0, so 2494 is a divisor of 2494)

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 2494 (i.e. 49.939963956735). 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 $\frac{N}{d} = D$ )

2494 / 1 = 2494 (the remainder is 0, so 1 and 2494 are divisors of 2494)
2494 / 2 = 1247 (the remainder is 0, so 2 and 1247 are divisors of 2494)
2494 / 3 = 831.33333333333 (the remainder is 1, so 3 is not a divisor of 2494)
...
2494 / 48 = 51.958333333333 (the remainder is 46, so 48 is not a divisor of 2494)
2494 / 49 = 50.897959183673 (the remainder is 44, so 49 is not a divisor of 2494)