What are the divisors of 2482?

1, 2, 17, 34, 73, 146, 1241, 2482

There is a total of 8 positive divisors.
The sum of these divisors is 3996.
The arithmetic mean is 499.5.

4 even divisors

2, 34, 146, 2482

4 odd divisors

1, 17, 73, 1241

How to compute the divisors of 2482?

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 2482 by each of the numbers from 1 to 2482 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)

2482 / 1 = 2482 (the remainder is 0, so 1 is a divisor of 2482)
2482 / 2 = 1241 (the remainder is 0, so 2 is a divisor of 2482)
2482 / 3 = 827.33333333333 (the remainder is 1, so 3 is not a divisor of 2482)
...
2482 / 2481 = 1.0004030632809 (the remainder is 1, so 2481 is not a divisor of 2482)
2482 / 2482 = 1 (the remainder is 0, so 2482 is a divisor of 2482)

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 2482 (i.e. 49.819674828325). 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 $\frac{N}{d} = D$ )

2482 / 1 = 2482 (the remainder is 0, so 1 and 2482 are divisors of 2482)
2482 / 2 = 1241 (the remainder is 0, so 2 and 1241 are divisors of 2482)
2482 / 3 = 827.33333333333 (the remainder is 1, so 3 is not a divisor of 2482)
...
2482 / 48 = 51.708333333333 (the remainder is 34, so 48 is not a divisor of 2482)
2482 / 49 = 50.65306122449 (the remainder is 32, so 49 is not a divisor of 2482)