What are the divisors of 6098?

1, 2, 3049, 6098

There is a total of 4 positive divisors.
The sum of these divisors is 9150.
The arithmetic mean is 2287.5.

2 even divisors

2, 6098

2 odd divisors

1, 3049

How to compute the divisors of 6098?

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 6098 by each of the numbers from 1 to 6098 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)

6098 / 1 = 6098 (the remainder is 0, so 1 is a divisor of 6098)
6098 / 2 = 3049 (the remainder is 0, so 2 is a divisor of 6098)
6098 / 3 = 2032.6666666667 (the remainder is 2, so 3 is not a divisor of 6098)
...
6098 / 6097 = 1.0001640150894 (the remainder is 1, so 6097 is not a divisor of 6098)
6098 / 6098 = 1 (the remainder is 0, so 6098 is a divisor of 6098)

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 6098 (i.e. 78.089692021419). 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 $\frac{N}{d} = D$ )

6098 / 1 = 6098 (the remainder is 0, so 1 and 6098 are divisors of 6098)
6098 / 2 = 3049 (the remainder is 0, so 2 and 3049 are divisors of 6098)
6098 / 3 = 2032.6666666667 (the remainder is 2, so 3 is not a divisor of 6098)
...
6098 / 77 = 79.194805194805 (the remainder is 15, so 77 is not a divisor of 6098)
6098 / 78 = 78.179487179487 (the remainder is 14, so 78 is not a divisor of 6098)