What are the divisors of 8152?

1, 2, 4, 8, 1019, 2038, 4076, 8152

There is a total of 8 positive divisors.
The sum of these divisors is 15300.
The arithmetic mean is 1912.5.

6 even divisors

2, 4, 8, 2038, 4076, 8152

2 odd divisors

1, 1019

How to compute the divisors of 8152?

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 8152 by each of the numbers from 1 to 8152 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)

8152 / 1 = 8152 (the remainder is 0, so 1 is a divisor of 8152)
8152 / 2 = 4076 (the remainder is 0, so 2 is a divisor of 8152)
8152 / 3 = 2717.3333333333 (the remainder is 1, so 3 is not a divisor of 8152)
...
8152 / 8151 = 1.0001226843332 (the remainder is 1, so 8151 is not a divisor of 8152)
8152 / 8152 = 1 (the remainder is 0, so 8152 is a divisor of 8152)

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 8152 (i.e. 90.288426722366). 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 $\frac{N}{d} = D$ )

8152 / 1 = 8152 (the remainder is 0, so 1 and 8152 are divisors of 8152)
8152 / 2 = 4076 (the remainder is 0, so 2 and 4076 are divisors of 8152)
8152 / 3 = 2717.3333333333 (the remainder is 1, so 3 is not a divisor of 8152)
...
8152 / 89 = 91.595505617978 (the remainder is 53, so 89 is not a divisor of 8152)
8152 / 90 = 90.577777777778 (the remainder is 52, so 90 is not a divisor of 8152)