What are the divisors of 8132?

1, 2, 4, 19, 38, 76, 107, 214, 428, 2033, 4066, 8132

There is a total of 12 positive divisors.
The sum of these divisors is 15120.
The arithmetic mean is 1260.

8 even divisors

2, 4, 38, 76, 214, 428, 4066, 8132

4 odd divisors

1, 19, 107, 2033

How to compute the divisors of 8132?

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 8132 by each of the numbers from 1 to 8132 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)

8132 / 1 = 8132 (the remainder is 0, so 1 is a divisor of 8132)
8132 / 2 = 4066 (the remainder is 0, so 2 is a divisor of 8132)
8132 / 3 = 2710.6666666667 (the remainder is 2, so 3 is not a divisor of 8132)
...
8132 / 8131 = 1.0001229861026 (the remainder is 1, so 8131 is not a divisor of 8132)
8132 / 8132 = 1 (the remainder is 0, so 8132 is a divisor of 8132)

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 8132 (i.e. 90.177602540764). 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 $\frac{N}{d} = D$ )

8132 / 1 = 8132 (the remainder is 0, so 1 and 8132 are divisors of 8132)
8132 / 2 = 4066 (the remainder is 0, so 2 and 4066 are divisors of 8132)
8132 / 3 = 2710.6666666667 (the remainder is 2, so 3 is not a divisor of 8132)
...
8132 / 89 = 91.370786516854 (the remainder is 33, so 89 is not a divisor of 8132)
8132 / 90 = 90.355555555556 (the remainder is 32, so 90 is not a divisor of 8132)