What are the divisors of 8292?

1, 2, 3, 4, 6, 12, 691, 1382, 2073, 2764, 4146, 8292

There is a total of 12 positive divisors.
The sum of these divisors is 19376.
The arithmetic mean is 1614.6666666667.

8 even divisors

2, 4, 6, 12, 1382, 2764, 4146, 8292

4 odd divisors

1, 3, 691, 2073

How to compute the divisors of 8292?

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 8292 by each of the numbers from 1 to 8292 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)

8292 / 1 = 8292 (the remainder is 0, so 1 is a divisor of 8292)
8292 / 2 = 4146 (the remainder is 0, so 2 is a divisor of 8292)
8292 / 3 = 2764 (the remainder is 0, so 3 is a divisor of 8292)
...
8292 / 8291 = 1.0001206127126 (the remainder is 1, so 8291 is not a divisor of 8292)
8292 / 8292 = 1 (the remainder is 0, so 8292 is a divisor of 8292)

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 8292 (i.e. 91.060419502658). 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 $\frac{N}{d} = D$ )

8292 / 1 = 8292 (the remainder is 0, so 1 and 8292 are divisors of 8292)
8292 / 2 = 4146 (the remainder is 0, so 2 and 4146 are divisors of 8292)
8292 / 3 = 2764 (the remainder is 0, so 3 and 2764 are divisors of 8292)
...
8292 / 90 = 92.133333333333 (the remainder is 12, so 90 is not a divisor of 8292)
8292 / 91 = 91.120879120879 (the remainder is 11, so 91 is not a divisor of 8292)