What are the divisors of 8246?

1, 2, 7, 14, 19, 31, 38, 62, 133, 217, 266, 434, 589, 1178, 4123, 8246

There is a total of 16 positive divisors.
The sum of these divisors is 15360.
The arithmetic mean is 960.

8 even divisors

2, 14, 38, 62, 266, 434, 1178, 8246

8 odd divisors

1, 7, 19, 31, 133, 217, 589, 4123

How to compute the divisors of 8246?

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 8246 by each of the numbers from 1 to 8246 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)

8246 / 1 = 8246 (the remainder is 0, so 1 is a divisor of 8246)
8246 / 2 = 4123 (the remainder is 0, so 2 is a divisor of 8246)
8246 / 3 = 2748.6666666667 (the remainder is 2, so 3 is not a divisor of 8246)
...
8246 / 8245 = 1.0001212856277 (the remainder is 1, so 8245 is not a divisor of 8246)
8246 / 8246 = 1 (the remainder is 0, so 8246 is a divisor of 8246)

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 8246 (i.e. 90.807488677972). 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 $\frac{N}{d} = D$ )

8246 / 1 = 8246 (the remainder is 0, so 1 and 8246 are divisors of 8246)
8246 / 2 = 4123 (the remainder is 0, so 2 and 4123 are divisors of 8246)
8246 / 3 = 2748.6666666667 (the remainder is 2, so 3 is not a divisor of 8246)
...
8246 / 89 = 92.651685393258 (the remainder is 58, so 89 is not a divisor of 8246)
8246 / 90 = 91.622222222222 (the remainder is 56, so 90 is not a divisor of 8246)