What are the divisors of 8057?

1, 7, 1151, 8057

There is a total of 4 positive divisors.
The sum of these divisors is 9216.
The arithmetic mean is 2304.

4 odd divisors

1, 7, 1151, 8057

How to compute the divisors of 8057?

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 8057 by each of the numbers from 1 to 8057 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)

8057 / 1 = 8057 (the remainder is 0, so 1 is a divisor of 8057)
8057 / 2 = 4028.5 (the remainder is 1, so 2 is not a divisor of 8057)
8057 / 3 = 2685.6666666667 (the remainder is 2, so 3 is not a divisor of 8057)
...
8057 / 8056 = 1.0001241310824 (the remainder is 1, so 8056 is not a divisor of 8057)
8057 / 8057 = 1 (the remainder is 0, so 8057 is a divisor of 8057)

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 8057 (i.e. 89.760793222877). 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 $\frac{N}{d} = D$ )

8057 / 1 = 8057 (the remainder is 0, so 1 and 8057 are divisors of 8057)
8057 / 2 = 4028.5 (the remainder is 1, so 2 is not a divisor of 8057)
8057 / 3 = 2685.6666666667 (the remainder is 2, so 3 is not a divisor of 8057)
...
8057 / 88 = 91.556818181818 (the remainder is 49, so 88 is not a divisor of 8057)
8057 / 89 = 90.52808988764 (the remainder is 47, so 89 is not a divisor of 8057)