What are the divisors of 2489?

1, 19, 131, 2489

There is a total of 4 positive divisors.
The sum of these divisors is 2640.
The arithmetic mean is 660.

4 odd divisors

1, 19, 131, 2489

How to compute the divisors of 2489?

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 2489 by each of the numbers from 1 to 2489 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)

2489 / 1 = 2489 (the remainder is 0, so 1 is a divisor of 2489)
2489 / 2 = 1244.5 (the remainder is 1, so 2 is not a divisor of 2489)
2489 / 3 = 829.66666666667 (the remainder is 2, so 3 is not a divisor of 2489)
...
2489 / 2488 = 1.0004019292605 (the remainder is 1, so 2488 is not a divisor of 2489)
2489 / 2489 = 1 (the remainder is 0, so 2489 is a divisor of 2489)

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 2489 (i.e. 49.889878733066). 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 $\frac{N}{d} = D$ )

2489 / 1 = 2489 (the remainder is 0, so 1 and 2489 are divisors of 2489)
2489 / 2 = 1244.5 (the remainder is 1, so 2 is not a divisor of 2489)
2489 / 3 = 829.66666666667 (the remainder is 2, so 3 is not a divisor of 2489)
...
2489 / 48 = 51.854166666667 (the remainder is 41, so 48 is not a divisor of 2489)
2489 / 49 = 50.795918367347 (the remainder is 39, so 49 is not a divisor of 2489)