What are the divisors of 8194?

1, 2, 17, 34, 241, 482, 4097, 8194

There is a total of 8 positive divisors.
The sum of these divisors is 13068.
The arithmetic mean is 1633.5.

4 even divisors

2, 34, 482, 8194

4 odd divisors

1, 17, 241, 4097

How to compute the divisors of 8194?

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 8194 by each of the numbers from 1 to 8194 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)

8194 / 1 = 8194 (the remainder is 0, so 1 is a divisor of 8194)
8194 / 2 = 4097 (the remainder is 0, so 2 is a divisor of 8194)
8194 / 3 = 2731.3333333333 (the remainder is 1, so 3 is not a divisor of 8194)
...
8194 / 8193 = 1.0001220554132 (the remainder is 1, so 8193 is not a divisor of 8194)
8194 / 8194 = 1 (the remainder is 0, so 8194 is a divisor of 8194)

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 8194 (i.e. 90.520715861067). 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 $\frac{N}{d} = D$ )

8194 / 1 = 8194 (the remainder is 0, so 1 and 8194 are divisors of 8194)
8194 / 2 = 4097 (the remainder is 0, so 2 and 4097 are divisors of 8194)
8194 / 3 = 2731.3333333333 (the remainder is 1, so 3 is not a divisor of 8194)
...
8194 / 89 = 92.067415730337 (the remainder is 6, so 89 is not a divisor of 8194)
8194 / 90 = 91.044444444444 (the remainder is 4, so 90 is not a divisor of 8194)