What are the divisors of 8102?

1, 2, 4051, 8102

There is a total of 4 positive divisors.
The sum of these divisors is 12156.
The arithmetic mean is 3039.

2 even divisors

2, 8102

2 odd divisors

1, 4051

How to compute the divisors of 8102?

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 8102 by each of the numbers from 1 to 8102 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)

8102 / 1 = 8102 (the remainder is 0, so 1 is a divisor of 8102)
8102 / 2 = 4051 (the remainder is 0, so 2 is a divisor of 8102)
8102 / 3 = 2700.6666666667 (the remainder is 2, so 3 is not a divisor of 8102)
...
8102 / 8101 = 1.0001234415504 (the remainder is 1, so 8101 is not a divisor of 8102)
8102 / 8102 = 1 (the remainder is 0, so 8102 is a divisor of 8102)

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 8102 (i.e. 90.011110425325). 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 $\frac{N}{d} = D$ )

8102 / 1 = 8102 (the remainder is 0, so 1 and 8102 are divisors of 8102)
8102 / 2 = 4051 (the remainder is 0, so 2 and 4051 are divisors of 8102)
8102 / 3 = 2700.6666666667 (the remainder is 2, so 3 is not a divisor of 8102)
...
8102 / 89 = 91.033707865169 (the remainder is 3, so 89 is not a divisor of 8102)
8102 / 90 = 90.022222222222 (the remainder is 2, so 90 is not a divisor of 8102)