What are the divisors of 8202?

1, 2, 3, 6, 1367, 2734, 4101, 8202

There is a total of 8 positive divisors.
The sum of these divisors is 16416.
The arithmetic mean is 2052.

4 even divisors

2, 6, 2734, 8202

4 odd divisors

1, 3, 1367, 4101

How to compute the divisors of 8202?

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 8202 by each of the numbers from 1 to 8202 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)

8202 / 1 = 8202 (the remainder is 0, so 1 is a divisor of 8202)
8202 / 2 = 4101 (the remainder is 0, so 2 is a divisor of 8202)
8202 / 3 = 2734 (the remainder is 0, so 3 is a divisor of 8202)
...
8202 / 8201 = 1.0001219363492 (the remainder is 1, so 8201 is not a divisor of 8202)
8202 / 8202 = 1 (the remainder is 0, so 8202 is a divisor of 8202)

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 8202 (i.e. 90.564893860701). 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 $\frac{N}{d} = D$ )

8202 / 1 = 8202 (the remainder is 0, so 1 and 8202 are divisors of 8202)
8202 / 2 = 4101 (the remainder is 0, so 2 and 4101 are divisors of 8202)
8202 / 3 = 2734 (the remainder is 0, so 3 and 2734 are divisors of 8202)
...
8202 / 89 = 92.157303370787 (the remainder is 14, so 89 is not a divisor of 8202)
8202 / 90 = 91.133333333333 (the remainder is 12, so 90 is not a divisor of 8202)