What are the divisors of 8156?

1, 2, 4, 2039, 4078, 8156

There is a total of 6 positive divisors.
The sum of these divisors is 14280.
The arithmetic mean is 2380.

4 even divisors

2, 4, 4078, 8156

2 odd divisors

1, 2039

How to compute the divisors of 8156?

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 8156 by each of the numbers from 1 to 8156 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)

8156 / 1 = 8156 (the remainder is 0, so 1 is a divisor of 8156)
8156 / 2 = 4078 (the remainder is 0, so 2 is a divisor of 8156)
8156 / 3 = 2718.6666666667 (the remainder is 2, so 3 is not a divisor of 8156)
...
8156 / 8155 = 1.000122624157 (the remainder is 1, so 8155 is not a divisor of 8156)
8156 / 8156 = 1 (the remainder is 0, so 8156 is a divisor of 8156)

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 8156 (i.e. 90.310575239005). 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 $\frac{N}{d} = D$ )

8156 / 1 = 8156 (the remainder is 0, so 1 and 8156 are divisors of 8156)
8156 / 2 = 4078 (the remainder is 0, so 2 and 4078 are divisors of 8156)
8156 / 3 = 2718.6666666667 (the remainder is 2, so 3 is not a divisor of 8156)
...
8156 / 89 = 91.640449438202 (the remainder is 57, so 89 is not a divisor of 8156)
8156 / 90 = 90.622222222222 (the remainder is 56, so 90 is not a divisor of 8156)