What are the divisors of 8154?

1, 2, 3, 6, 9, 18, 27, 54, 151, 302, 453, 906, 1359, 2718, 4077, 8154

There is a total of 16 positive divisors.
The sum of these divisors is 18240.
The arithmetic mean is 1140.

8 even divisors

2, 6, 18, 54, 302, 906, 2718, 8154

8 odd divisors

1, 3, 9, 27, 151, 453, 1359, 4077

How to compute the divisors of 8154?

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 8154 by each of the numbers from 1 to 8154 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)

8154 / 1 = 8154 (the remainder is 0, so 1 is a divisor of 8154)
8154 / 2 = 4077 (the remainder is 0, so 2 is a divisor of 8154)
8154 / 3 = 2718 (the remainder is 0, so 3 is a divisor of 8154)
...
8154 / 8153 = 1.0001226542377 (the remainder is 1, so 8153 is not a divisor of 8154)
8154 / 8154 = 1 (the remainder is 0, so 8154 is a divisor of 8154)

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 8154 (i.e. 90.299501659754). 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 $\frac{N}{d} = D$ )

8154 / 1 = 8154 (the remainder is 0, so 1 and 8154 are divisors of 8154)
8154 / 2 = 4077 (the remainder is 0, so 2 and 4077 are divisors of 8154)
8154 / 3 = 2718 (the remainder is 0, so 3 and 2718 are divisors of 8154)
...
8154 / 89 = 91.61797752809 (the remainder is 55, so 89 is not a divisor of 8154)
8154 / 90 = 90.6 (the remainder is 54, so 90 is not a divisor of 8154)