What are the divisors of 8296?

1, 2, 4, 8, 17, 34, 61, 68, 122, 136, 244, 488, 1037, 2074, 4148, 8296

There is a total of 16 positive divisors.
The sum of these divisors is 16740.
The arithmetic mean is 1046.25.

12 even divisors

2, 4, 8, 34, 68, 122, 136, 244, 488, 2074, 4148, 8296

4 odd divisors

1, 17, 61, 1037

How to compute the divisors of 8296?

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 8296 by each of the numbers from 1 to 8296 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)

8296 / 1 = 8296 (the remainder is 0, so 1 is a divisor of 8296)
8296 / 2 = 4148 (the remainder is 0, so 2 is a divisor of 8296)
8296 / 3 = 2765.3333333333 (the remainder is 1, so 3 is not a divisor of 8296)
...
8296 / 8295 = 1.0001205545509 (the remainder is 1, so 8295 is not a divisor of 8296)
8296 / 8296 = 1 (the remainder is 0, so 8296 is a divisor of 8296)

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 8296 (i.e. 91.082380293886). 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 $\frac{N}{d} = D$ )

8296 / 1 = 8296 (the remainder is 0, so 1 and 8296 are divisors of 8296)
8296 / 2 = 4148 (the remainder is 0, so 2 and 4148 are divisors of 8296)
8296 / 3 = 2765.3333333333 (the remainder is 1, so 3 is not a divisor of 8296)
...
8296 / 90 = 92.177777777778 (the remainder is 16, so 90 is not a divisor of 8296)
8296 / 91 = 91.164835164835 (the remainder is 15, so 91 is not a divisor of 8296)