What are the divisors of 8155?

1, 5, 7, 35, 233, 1165, 1631, 8155

There is a total of 8 positive divisors.
The sum of these divisors is 11232.
The arithmetic mean is 1404.

8 odd divisors

1, 5, 7, 35, 233, 1165, 1631, 8155

How to compute the divisors of 8155?

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 8155 by each of the numbers from 1 to 8155 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)

8155 / 1 = 8155 (the remainder is 0, so 1 is a divisor of 8155)
8155 / 2 = 4077.5 (the remainder is 1, so 2 is not a divisor of 8155)
8155 / 3 = 2718.3333333333 (the remainder is 1, so 3 is not a divisor of 8155)
...
8155 / 8154 = 1.0001226391955 (the remainder is 1, so 8154 is not a divisor of 8155)
8155 / 8155 = 1 (the remainder is 0, so 8155 is a divisor of 8155)

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 8155 (i.e. 90.305038619116). 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 $\frac{N}{d} = D$ )

8155 / 1 = 8155 (the remainder is 0, so 1 and 8155 are divisors of 8155)
8155 / 2 = 4077.5 (the remainder is 1, so 2 is not a divisor of 8155)
8155 / 3 = 2718.3333333333 (the remainder is 1, so 3 is not a divisor of 8155)
...
8155 / 89 = 91.629213483146 (the remainder is 56, so 89 is not a divisor of 8155)
8155 / 90 = 90.611111111111 (the remainder is 55, so 90 is not a divisor of 8155)