What are the divisors of 8232?

1, 2, 3, 4, 6, 7, 8, 12, 14, 21, 24, 28, 42, 49, 56, 84, 98, 147, 168, 196, 294, 343, 392, 588, 686, 1029, 1176, 1372, 2058, 2744, 4116, 8232

There is a total of 32 positive divisors.
The sum of these divisors is 24000.
The arithmetic mean is 750.

24 even divisors

2, 4, 6, 8, 12, 14, 24, 28, 42, 56, 84, 98, 168, 196, 294, 392, 588, 686, 1176, 1372, 2058, 2744, 4116, 8232

8 odd divisors

1, 3, 7, 21, 49, 147, 343, 1029

How to compute the divisors of 8232?

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 8232 by each of the numbers from 1 to 8232 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)

8232 / 1 = 8232 (the remainder is 0, so 1 is a divisor of 8232)
8232 / 2 = 4116 (the remainder is 0, so 2 is a divisor of 8232)
8232 / 3 = 2744 (the remainder is 0, so 3 is a divisor of 8232)
...
8232 / 8231 = 1.0001214919208 (the remainder is 1, so 8231 is not a divisor of 8232)
8232 / 8232 = 1 (the remainder is 0, so 8232 is a divisor of 8232)

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 8232 (i.e. 90.73036977771). 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 $\frac{N}{d} = D$ )

8232 / 1 = 8232 (the remainder is 0, so 1 and 8232 are divisors of 8232)
8232 / 2 = 4116 (the remainder is 0, so 2 and 4116 are divisors of 8232)
8232 / 3 = 2744 (the remainder is 0, so 3 and 2744 are divisors of 8232)
...
8232 / 89 = 92.494382022472 (the remainder is 44, so 89 is not a divisor of 8232)
8232 / 90 = 91.466666666667 (the remainder is 42, so 90 is not a divisor of 8232)