What are the divisors of 4082?

1, 2, 13, 26, 157, 314, 2041, 4082

There is a total of 8 positive divisors.
The sum of these divisors is 6636.
The arithmetic mean is 829.5.

4 even divisors

2, 26, 314, 4082

4 odd divisors

1, 13, 157, 2041

How to compute the divisors of 4082?

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 4082 by each of the numbers from 1 to 4082 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)

4082 / 1 = 4082 (the remainder is 0, so 1 is a divisor of 4082)
4082 / 2 = 2041 (the remainder is 0, so 2 is a divisor of 4082)
4082 / 3 = 1360.6666666667 (the remainder is 2, so 3 is not a divisor of 4082)
...
4082 / 4081 = 1.0002450379809 (the remainder is 1, so 4081 is not a divisor of 4082)
4082 / 4082 = 1 (the remainder is 0, so 4082 is a divisor of 4082)

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 4082 (i.e. 63.890531379853). 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 $\frac{N}{d} = D$ )

4082 / 1 = 4082 (the remainder is 0, so 1 and 4082 are divisors of 4082)
4082 / 2 = 2041 (the remainder is 0, so 2 and 2041 are divisors of 4082)
4082 / 3 = 1360.6666666667 (the remainder is 2, so 3 is not a divisor of 4082)
...
4082 / 62 = 65.838709677419 (the remainder is 52, so 62 is not a divisor of 4082)
4082 / 63 = 64.793650793651 (the remainder is 50, so 63 is not a divisor of 4082)