What are the divisors of 8276?

1, 2, 4, 2069, 4138, 8276

There is a total of 6 positive divisors.
The sum of these divisors is 14490.
The arithmetic mean is 2415.

4 even divisors

2, 4, 4138, 8276

2 odd divisors

1, 2069

How to compute the divisors of 8276?

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 8276 by each of the numbers from 1 to 8276 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)

8276 / 1 = 8276 (the remainder is 0, so 1 is a divisor of 8276)
8276 / 2 = 4138 (the remainder is 0, so 2 is a divisor of 8276)
8276 / 3 = 2758.6666666667 (the remainder is 2, so 3 is not a divisor of 8276)
...
8276 / 8275 = 1.0001208459215 (the remainder is 1, so 8275 is not a divisor of 8276)
8276 / 8276 = 1 (the remainder is 0, so 8276 is a divisor of 8276)

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 8276 (i.e. 90.972523324353). 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 $\frac{N}{d} = D$ )

8276 / 1 = 8276 (the remainder is 0, so 1 and 8276 are divisors of 8276)
8276 / 2 = 4138 (the remainder is 0, so 2 and 4138 are divisors of 8276)
8276 / 3 = 2758.6666666667 (the remainder is 2, so 3 is not a divisor of 8276)
...
8276 / 89 = 92.988764044944 (the remainder is 88, so 89 is not a divisor of 8276)
8276 / 90 = 91.955555555556 (the remainder is 86, so 90 is not a divisor of 8276)