What are the divisors of 8249?

1, 73, 113, 8249

There is a total of 4 positive divisors.
The sum of these divisors is 8436.
The arithmetic mean is 2109.

4 odd divisors

1, 73, 113, 8249

How to compute the divisors of 8249?

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 8249 by each of the numbers from 1 to 8249 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)

8249 / 1 = 8249 (the remainder is 0, so 1 is a divisor of 8249)
8249 / 2 = 4124.5 (the remainder is 1, so 2 is not a divisor of 8249)
8249 / 3 = 2749.6666666667 (the remainder is 2, so 3 is not a divisor of 8249)
...
8249 / 8248 = 1.0001212415131 (the remainder is 1, so 8248 is not a divisor of 8249)
8249 / 8249 = 1 (the remainder is 0, so 8249 is a divisor of 8249)

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 8249 (i.e. 90.824005637276). 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 $\frac{N}{d} = D$ )

8249 / 1 = 8249 (the remainder is 0, so 1 and 8249 are divisors of 8249)
8249 / 2 = 4124.5 (the remainder is 1, so 2 is not a divisor of 8249)
8249 / 3 = 2749.6666666667 (the remainder is 2, so 3 is not a divisor of 8249)
...
8249 / 89 = 92.685393258427 (the remainder is 61, so 89 is not a divisor of 8249)
8249 / 90 = 91.655555555556 (the remainder is 59, so 90 is not a divisor of 8249)