What are the divisors of 8098?

1, 2, 4049, 8098

There is a total of 4 positive divisors.
The sum of these divisors is 12150.
The arithmetic mean is 3037.5.

2 even divisors

2, 8098

2 odd divisors

1, 4049

How to compute the divisors of 8098?

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 8098 by each of the numbers from 1 to 8098 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)

8098 / 1 = 8098 (the remainder is 0, so 1 is a divisor of 8098)
8098 / 2 = 4049 (the remainder is 0, so 2 is a divisor of 8098)
8098 / 3 = 2699.3333333333 (the remainder is 1, so 3 is not a divisor of 8098)
...
8098 / 8097 = 1.0001235025318 (the remainder is 1, so 8097 is not a divisor of 8098)
8098 / 8098 = 1 (the remainder is 0, so 8098 is a divisor of 8098)

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 8098 (i.e. 89.988888202933). 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 $\frac{N}{d} = D$ )

8098 / 1 = 8098 (the remainder is 0, so 1 and 8098 are divisors of 8098)
8098 / 2 = 4049 (the remainder is 0, so 2 and 4049 are divisors of 8098)
8098 / 3 = 2699.3333333333 (the remainder is 1, so 3 is not a divisor of 8098)
...
8098 / 88 = 92.022727272727 (the remainder is 2, so 88 is not a divisor of 8098)
8098 / 89 = 90.988764044944 (the remainder is 88, so 89 is not a divisor of 8098)