What are the divisors of 8077?

1, 41, 197, 8077

There is a total of 4 positive divisors.
The sum of these divisors is 8316.
The arithmetic mean is 2079.

4 odd divisors

1, 41, 197, 8077

How to compute the divisors of 8077?

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 8077 by each of the numbers from 1 to 8077 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)

8077 / 1 = 8077 (the remainder is 0, so 1 is a divisor of 8077)
8077 / 2 = 4038.5 (the remainder is 1, so 2 is not a divisor of 8077)
8077 / 3 = 2692.3333333333 (the remainder is 1, so 3 is not a divisor of 8077)
...
8077 / 8076 = 1.0001238236751 (the remainder is 1, so 8076 is not a divisor of 8077)
8077 / 8077 = 1 (the remainder is 0, so 8077 is a divisor of 8077)

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 8077 (i.e. 89.872131386765). 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 $\frac{N}{d} = D$ )

8077 / 1 = 8077 (the remainder is 0, so 1 and 8077 are divisors of 8077)
8077 / 2 = 4038.5 (the remainder is 1, so 2 is not a divisor of 8077)
8077 / 3 = 2692.3333333333 (the remainder is 1, so 3 is not a divisor of 8077)
...
8077 / 88 = 91.784090909091 (the remainder is 69, so 88 is not a divisor of 8077)
8077 / 89 = 90.752808988764 (the remainder is 67, so 89 is not a divisor of 8077)