What are the divisors of 8162?

1, 2, 7, 11, 14, 22, 53, 77, 106, 154, 371, 583, 742, 1166, 4081, 8162

There is a total of 16 positive divisors.
The sum of these divisors is 15552.
The arithmetic mean is 972.

8 even divisors

2, 14, 22, 106, 154, 742, 1166, 8162

8 odd divisors

1, 7, 11, 53, 77, 371, 583, 4081

How to compute the divisors of 8162?

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 8162 by each of the numbers from 1 to 8162 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)

8162 / 1 = 8162 (the remainder is 0, so 1 is a divisor of 8162)
8162 / 2 = 4081 (the remainder is 0, so 2 is a divisor of 8162)
8162 / 3 = 2720.6666666667 (the remainder is 2, so 3 is not a divisor of 8162)
...
8162 / 8161 = 1.0001225340032 (the remainder is 1, so 8161 is not a divisor of 8162)
8162 / 8162 = 1 (the remainder is 0, so 8162 is a divisor of 8162)

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 8162 (i.e. 90.343787832922). 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 $\frac{N}{d} = D$ )

8162 / 1 = 8162 (the remainder is 0, so 1 and 8162 are divisors of 8162)
8162 / 2 = 4081 (the remainder is 0, so 2 and 4081 are divisors of 8162)
8162 / 3 = 2720.6666666667 (the remainder is 2, so 3 is not a divisor of 8162)
...
8162 / 89 = 91.707865168539 (the remainder is 63, so 89 is not a divisor of 8162)
8162 / 90 = 90.688888888889 (the remainder is 62, so 90 is not a divisor of 8162)