What are the divisors of 2483?

1, 13, 191, 2483

There is a total of 4 positive divisors.
The sum of these divisors is 2688.
The arithmetic mean is 672.

4 odd divisors

1, 13, 191, 2483

How to compute the divisors of 2483?

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 2483 by each of the numbers from 1 to 2483 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)

2483 / 1 = 2483 (the remainder is 0, so 1 is a divisor of 2483)
2483 / 2 = 1241.5 (the remainder is 1, so 2 is not a divisor of 2483)
2483 / 3 = 827.66666666667 (the remainder is 2, so 3 is not a divisor of 2483)
...
2483 / 2482 = 1.0004029008864 (the remainder is 1, so 2482 is not a divisor of 2483)
2483 / 2483 = 1 (the remainder is 0, so 2483 is a divisor of 2483)

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 2483 (i.e. 49.829710013204). 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 $\frac{N}{d} = D$ )

2483 / 1 = 2483 (the remainder is 0, so 1 and 2483 are divisors of 2483)
2483 / 2 = 1241.5 (the remainder is 1, so 2 is not a divisor of 2483)
2483 / 3 = 827.66666666667 (the remainder is 2, so 3 is not a divisor of 2483)
...
2483 / 48 = 51.729166666667 (the remainder is 35, so 48 is not a divisor of 2483)
2483 / 49 = 50.673469387755 (the remainder is 33, so 49 is not a divisor of 2483)