What are the divisors of 8277?

1, 3, 31, 89, 93, 267, 2759, 8277

There is a total of 8 positive divisors.
The sum of these divisors is 11520.
The arithmetic mean is 1440.

8 odd divisors

1, 3, 31, 89, 93, 267, 2759, 8277

How to compute the divisors of 8277?

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 8277 by each of the numbers from 1 to 8277 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)

8277 / 1 = 8277 (the remainder is 0, so 1 is a divisor of 8277)
8277 / 2 = 4138.5 (the remainder is 1, so 2 is not a divisor of 8277)
8277 / 3 = 2759 (the remainder is 0, so 3 is a divisor of 8277)
...
8277 / 8276 = 1.0001208313195 (the remainder is 1, so 8276 is not a divisor of 8277)
8277 / 8277 = 1 (the remainder is 0, so 8277 is a divisor of 8277)

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 8277 (i.e. 90.978019323351). 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 $\frac{N}{d} = D$ )

8277 / 1 = 8277 (the remainder is 0, so 1 and 8277 are divisors of 8277)
8277 / 2 = 4138.5 (the remainder is 1, so 2 is not a divisor of 8277)
8277 / 3 = 2759 (the remainder is 0, so 3 and 2759 are divisors of 8277)
...
8277 / 89 = 93 (the remainder is 0, so 89 and 93 are divisors of 8277)
8277 / 90 = 91.966666666667 (the remainder is 87, so 90 is not a divisor of 8277)