What are the divisors of 8272?

1, 2, 4, 8, 11, 16, 22, 44, 47, 88, 94, 176, 188, 376, 517, 752, 1034, 2068, 4136, 8272

There is a total of 20 positive divisors.
The sum of these divisors is 17856.
The arithmetic mean is 892.8.

16 even divisors

2, 4, 8, 16, 22, 44, 88, 94, 176, 188, 376, 752, 1034, 2068, 4136, 8272

4 odd divisors

1, 11, 47, 517

How to compute the divisors of 8272?

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 8272 by each of the numbers from 1 to 8272 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)

8272 / 1 = 8272 (the remainder is 0, so 1 is a divisor of 8272)
8272 / 2 = 4136 (the remainder is 0, so 2 is a divisor of 8272)
8272 / 3 = 2757.3333333333 (the remainder is 1, so 3 is not a divisor of 8272)
...
8272 / 8271 = 1.0001209043646 (the remainder is 1, so 8271 is not a divisor of 8272)
8272 / 8272 = 1 (the remainder is 0, so 8272 is a divisor of 8272)

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 8272 (i.e. 90.950536007217). 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 $\frac{N}{d} = D$ )

8272 / 1 = 8272 (the remainder is 0, so 1 and 8272 are divisors of 8272)
8272 / 2 = 4136 (the remainder is 0, so 2 and 4136 are divisors of 8272)
8272 / 3 = 2757.3333333333 (the remainder is 1, so 3 is not a divisor of 8272)
...
8272 / 89 = 92.943820224719 (the remainder is 84, so 89 is not a divisor of 8272)
8272 / 90 = 91.911111111111 (the remainder is 82, so 90 is not a divisor of 8272)