What are the divisors of 8278?

1, 2, 4139, 8278

There is a total of 4 positive divisors.
The sum of these divisors is 12420.
The arithmetic mean is 3105.

2 even divisors

2, 8278

2 odd divisors

1, 4139

How to compute the divisors of 8278?

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 8278 by each of the numbers from 1 to 8278 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)

8278 / 1 = 8278 (the remainder is 0, so 1 is a divisor of 8278)
8278 / 2 = 4139 (the remainder is 0, so 2 is a divisor of 8278)
8278 / 3 = 2759.3333333333 (the remainder is 1, so 3 is not a divisor of 8278)
...
8278 / 8277 = 1.000120816721 (the remainder is 1, so 8277 is not a divisor of 8278)
8278 / 8278 = 1 (the remainder is 0, so 8278 is a divisor of 8278)

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 8278 (i.e. 90.983514990354). 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 $\frac{N}{d} = D$ )

8278 / 1 = 8278 (the remainder is 0, so 1 and 8278 are divisors of 8278)
8278 / 2 = 4139 (the remainder is 0, so 2 and 4139 are divisors of 8278)
8278 / 3 = 2759.3333333333 (the remainder is 1, so 3 is not a divisor of 8278)
...
8278 / 89 = 93.011235955056 (the remainder is 1, so 89 is not a divisor of 8278)
8278 / 90 = 91.977777777778 (the remainder is 88, so 90 is not a divisor of 8278)