What are the divisors of 8247?

1, 3, 2749, 8247

There is a total of 4 positive divisors.
The sum of these divisors is 11000.
The arithmetic mean is 2750.

4 odd divisors

1, 3, 2749, 8247

How to compute the divisors of 8247?

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 8247 by each of the numbers from 1 to 8247 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)

8247 / 1 = 8247 (the remainder is 0, so 1 is a divisor of 8247)
8247 / 2 = 4123.5 (the remainder is 1, so 2 is not a divisor of 8247)
8247 / 3 = 2749 (the remainder is 0, so 3 is a divisor of 8247)
...
8247 / 8246 = 1.0001212709192 (the remainder is 1, so 8246 is not a divisor of 8247)
8247 / 8247 = 1 (the remainder is 0, so 8247 is a divisor of 8247)

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 8247 (i.e. 90.812994664861). 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 $\frac{N}{d} = D$ )

8247 / 1 = 8247 (the remainder is 0, so 1 and 8247 are divisors of 8247)
8247 / 2 = 4123.5 (the remainder is 1, so 2 is not a divisor of 8247)
8247 / 3 = 2749 (the remainder is 0, so 3 and 2749 are divisors of 8247)
...
8247 / 89 = 92.662921348315 (the remainder is 59, so 89 is not a divisor of 8247)
8247 / 90 = 91.633333333333 (the remainder is 57, so 90 is not a divisor of 8247)