What are the divisors of 8294?

1, 2, 11, 13, 22, 26, 29, 58, 143, 286, 319, 377, 638, 754, 4147, 8294

There is a total of 16 positive divisors.
The sum of these divisors is 15120.
The arithmetic mean is 945.

8 even divisors

2, 22, 26, 58, 286, 638, 754, 8294

8 odd divisors

1, 11, 13, 29, 143, 319, 377, 4147

How to compute the divisors of 8294?

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 8294 by each of the numbers from 1 to 8294 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)

8294 / 1 = 8294 (the remainder is 0, so 1 is a divisor of 8294)
8294 / 2 = 4147 (the remainder is 0, so 2 is a divisor of 8294)
8294 / 3 = 2764.6666666667 (the remainder is 2, so 3 is not a divisor of 8294)
...
8294 / 8293 = 1.0001205836247 (the remainder is 1, so 8293 is not a divisor of 8294)
8294 / 8294 = 1 (the remainder is 0, so 8294 is a divisor of 8294)

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 8294 (i.e. 91.07140056022). 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 $\frac{N}{d} = D$ )

8294 / 1 = 8294 (the remainder is 0, so 1 and 8294 are divisors of 8294)
8294 / 2 = 4147 (the remainder is 0, so 2 and 4147 are divisors of 8294)
8294 / 3 = 2764.6666666667 (the remainder is 2, so 3 is not a divisor of 8294)
...
8294 / 90 = 92.155555555556 (the remainder is 14, so 90 is not a divisor of 8294)
8294 / 91 = 91.142857142857 (the remainder is 13, so 91 is not a divisor of 8294)