What are the divisors of 8284?

1, 2, 4, 19, 38, 76, 109, 218, 436, 2071, 4142, 8284

There is a total of 12 positive divisors.
The sum of these divisors is 15400.
The arithmetic mean is 1283.3333333333.

8 even divisors

2, 4, 38, 76, 218, 436, 4142, 8284

4 odd divisors

1, 19, 109, 2071

How to compute the divisors of 8284?

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 8284 by each of the numbers from 1 to 8284 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)

8284 / 1 = 8284 (the remainder is 0, so 1 is a divisor of 8284)
8284 / 2 = 4142 (the remainder is 0, so 2 is a divisor of 8284)
8284 / 3 = 2761.3333333333 (the remainder is 1, so 3 is not a divisor of 8284)
...
8284 / 8283 = 1.0001207292044 (the remainder is 1, so 8283 is not a divisor of 8284)
8284 / 8284 = 1 (the remainder is 0, so 8284 is a divisor of 8284)

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 8284 (i.e. 91.016482023862). 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 $\frac{N}{d} = D$ )

8284 / 1 = 8284 (the remainder is 0, so 1 and 8284 are divisors of 8284)
8284 / 2 = 4142 (the remainder is 0, so 2 and 4142 are divisors of 8284)
8284 / 3 = 2761.3333333333 (the remainder is 1, so 3 is not a divisor of 8284)
...
8284 / 90 = 92.044444444444 (the remainder is 4, so 90 is not a divisor of 8284)
8284 / 91 = 91.032967032967 (the remainder is 3, so 91 is not a divisor of 8284)