What are the divisors of 8047?

1, 13, 619, 8047

There is a total of 4 positive divisors.
The sum of these divisors is 8680.
The arithmetic mean is 2170.

4 odd divisors

1, 13, 619, 8047

How to compute the divisors of 8047?

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 8047 by each of the numbers from 1 to 8047 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)

8047 / 1 = 8047 (the remainder is 0, so 1 is a divisor of 8047)
8047 / 2 = 4023.5 (the remainder is 1, so 2 is not a divisor of 8047)
8047 / 3 = 2682.3333333333 (the remainder is 1, so 3 is not a divisor of 8047)
...
8047 / 8046 = 1.0001242853592 (the remainder is 1, so 8046 is not a divisor of 8047)
8047 / 8047 = 1 (the remainder is 0, so 8047 is a divisor of 8047)

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 8047 (i.e. 89.705072320354). 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 $\frac{N}{d} = D$ )

8047 / 1 = 8047 (the remainder is 0, so 1 and 8047 are divisors of 8047)
8047 / 2 = 4023.5 (the remainder is 1, so 2 is not a divisor of 8047)
8047 / 3 = 2682.3333333333 (the remainder is 1, so 3 is not a divisor of 8047)
...
8047 / 88 = 91.443181818182 (the remainder is 39, so 88 is not a divisor of 8047)
8047 / 89 = 90.415730337079 (the remainder is 37, so 89 is not a divisor of 8047)