What are the divisors of 8147?

1, 8147

There is a total of 2 positive divisors.
The sum of these divisors is 8148.
The arithmetic mean is 4074.

2 odd divisors

1, 8147

How to compute the divisors of 8147?

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 8147 by each of the numbers from 1 to 8147 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)

8147 / 1 = 8147 (the remainder is 0, so 1 is a divisor of 8147)
8147 / 2 = 4073.5 (the remainder is 1, so 2 is not a divisor of 8147)
8147 / 3 = 2715.6666666667 (the remainder is 2, so 3 is not a divisor of 8147)
...
8147 / 8146 = 1.0001227596366 (the remainder is 1, so 8146 is not a divisor of 8147)
8147 / 8147 = 1 (the remainder is 0, so 8147 is a divisor of 8147)

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 8147 (i.e. 90.260733433758). 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 $\frac{N}{d} = D$ )

8147 / 1 = 8147 (the remainder is 0, so 1 and 8147 are divisors of 8147)
8147 / 2 = 4073.5 (the remainder is 1, so 2 is not a divisor of 8147)
8147 / 3 = 2715.6666666667 (the remainder is 2, so 3 is not a divisor of 8147)
...
8147 / 89 = 91.539325842697 (the remainder is 48, so 89 is not a divisor of 8147)
8147 / 90 = 90.522222222222 (the remainder is 47, so 90 is not a divisor of 8147)