What are the divisors of 5098?

1, 2, 2549, 5098

There is a total of 4 positive divisors.
The sum of these divisors is 7650.
The arithmetic mean is 1912.5.

2 even divisors

2, 5098

2 odd divisors

1, 2549

How to compute the divisors of 5098?

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 5098 by each of the numbers from 1 to 5098 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)

5098 / 1 = 5098 (the remainder is 0, so 1 is a divisor of 5098)
5098 / 2 = 2549 (the remainder is 0, so 2 is a divisor of 5098)
5098 / 3 = 1699.3333333333 (the remainder is 1, so 3 is not a divisor of 5098)
...
5098 / 5097 = 1.0001961938395 (the remainder is 1, so 5097 is not a divisor of 5098)
5098 / 5098 = 1 (the remainder is 0, so 5098 is a divisor of 5098)

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 5098 (i.e. 71.400280111495). 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 $\frac{N}{d} = D$ )

5098 / 1 = 5098 (the remainder is 0, so 1 and 5098 are divisors of 5098)
5098 / 2 = 2549 (the remainder is 0, so 2 and 2549 are divisors of 5098)
5098 / 3 = 1699.3333333333 (the remainder is 1, so 3 is not a divisor of 5098)
...
5098 / 70 = 72.828571428571 (the remainder is 58, so 70 is not a divisor of 5098)
5098 / 71 = 71.802816901408 (the remainder is 57, so 71 is not a divisor of 5098)