What are the divisors of 8054?

1, 2, 4027, 8054

There is a total of 4 positive divisors.
The sum of these divisors is 12084.
The arithmetic mean is 3021.

2 even divisors

2, 8054

2 odd divisors

1, 4027

How to compute the divisors of 8054?

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 8054 by each of the numbers from 1 to 8054 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)

8054 / 1 = 8054 (the remainder is 0, so 1 is a divisor of 8054)
8054 / 2 = 4027 (the remainder is 0, so 2 is a divisor of 8054)
8054 / 3 = 2684.6666666667 (the remainder is 2, so 3 is not a divisor of 8054)
...
8054 / 8053 = 1.0001241773252 (the remainder is 1, so 8053 is not a divisor of 8054)
8054 / 8054 = 1 (the remainder is 0, so 8054 is a divisor of 8054)

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 8054 (i.e. 89.744080584738). 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 $\frac{N}{d} = D$ )

8054 / 1 = 8054 (the remainder is 0, so 1 and 8054 are divisors of 8054)
8054 / 2 = 4027 (the remainder is 0, so 2 and 4027 are divisors of 8054)
8054 / 3 = 2684.6666666667 (the remainder is 2, so 3 is not a divisor of 8054)
...
8054 / 88 = 91.522727272727 (the remainder is 46, so 88 is not a divisor of 8054)
8054 / 89 = 90.494382022472 (the remainder is 44, so 89 is not a divisor of 8054)