What are the divisors of 8074?

1, 2, 11, 22, 367, 734, 4037, 8074

There is a total of 8 positive divisors.
The sum of these divisors is 13248.
The arithmetic mean is 1656.

4 even divisors

2, 22, 734, 8074

4 odd divisors

1, 11, 367, 4037

How to compute the divisors of 8074?

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 8074 by each of the numbers from 1 to 8074 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)

8074 / 1 = 8074 (the remainder is 0, so 1 is a divisor of 8074)
8074 / 2 = 4037 (the remainder is 0, so 2 is a divisor of 8074)
8074 / 3 = 2691.3333333333 (the remainder is 1, so 3 is not a divisor of 8074)
...
8074 / 8073 = 1.0001238696891 (the remainder is 1, so 8073 is not a divisor of 8074)
8074 / 8074 = 1 (the remainder is 0, so 8074 is a divisor of 8074)

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 8074 (i.e. 89.855439456941). 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 $\frac{N}{d} = D$ )

8074 / 1 = 8074 (the remainder is 0, so 1 and 8074 are divisors of 8074)
8074 / 2 = 4037 (the remainder is 0, so 2 and 4037 are divisors of 8074)
8074 / 3 = 2691.3333333333 (the remainder is 1, so 3 is not a divisor of 8074)
...
8074 / 88 = 91.75 (the remainder is 66, so 88 is not a divisor of 8074)
8074 / 89 = 90.719101123596 (the remainder is 64, so 89 is not a divisor of 8074)