What are the divisors of 9098?

1, 2, 4549, 9098

There is a total of 4 positive divisors.
The sum of these divisors is 13650.
The arithmetic mean is 3412.5.

2 even divisors

2, 9098

2 odd divisors

1, 4549

How to compute the divisors of 9098?

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 9098 by each of the numbers from 1 to 9098 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)

9098 / 1 = 9098 (the remainder is 0, so 1 is a divisor of 9098)
9098 / 2 = 4549 (the remainder is 0, so 2 is a divisor of 9098)
9098 / 3 = 3032.6666666667 (the remainder is 2, so 3 is not a divisor of 9098)
...
9098 / 9097 = 1.0001099263493 (the remainder is 1, so 9097 is not a divisor of 9098)
9098 / 9098 = 1 (the remainder is 0, so 9098 is a divisor of 9098)

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 9098 (i.e. 95.383436717283). 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 $\frac{N}{d} = D$ )

9098 / 1 = 9098 (the remainder is 0, so 1 and 9098 are divisors of 9098)
9098 / 2 = 4549 (the remainder is 0, so 2 and 4549 are divisors of 9098)
9098 / 3 = 3032.6666666667 (the remainder is 2, so 3 is not a divisor of 9098)
...
9098 / 94 = 96.787234042553 (the remainder is 74, so 94 is not a divisor of 9098)
9098 / 95 = 95.768421052632 (the remainder is 73, so 95 is not a divisor of 9098)