What are the divisors of 8264?

1, 2, 4, 8, 1033, 2066, 4132, 8264

There is a total of 8 positive divisors.
The sum of these divisors is 15510.
The arithmetic mean is 1938.75.

6 even divisors

2, 4, 8, 2066, 4132, 8264

2 odd divisors

1, 1033

How to compute the divisors of 8264?

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 8264 by each of the numbers from 1 to 8264 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)

8264 / 1 = 8264 (the remainder is 0, so 1 is a divisor of 8264)
8264 / 2 = 4132 (the remainder is 0, so 2 is a divisor of 8264)
8264 / 3 = 2754.6666666667 (the remainder is 2, so 3 is not a divisor of 8264)
...
8264 / 8263 = 1.0001210214208 (the remainder is 1, so 8263 is not a divisor of 8264)
8264 / 8264 = 1 (the remainder is 0, so 8264 is a divisor of 8264)

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 8264 (i.e. 90.906545418908). 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 $\frac{N}{d} = D$ )

8264 / 1 = 8264 (the remainder is 0, so 1 and 8264 are divisors of 8264)
8264 / 2 = 4132 (the remainder is 0, so 2 and 4132 are divisors of 8264)
8264 / 3 = 2754.6666666667 (the remainder is 2, so 3 is not a divisor of 8264)
...
8264 / 89 = 92.85393258427 (the remainder is 76, so 89 is not a divisor of 8264)
8264 / 90 = 91.822222222222 (the remainder is 74, so 90 is not a divisor of 8264)