What are the divisors of 3082?

1, 2, 23, 46, 67, 134, 1541, 3082

There is a total of 8 positive divisors.
The sum of these divisors is 4896.
The arithmetic mean is 612.

4 even divisors

2, 46, 134, 3082

4 odd divisors

1, 23, 67, 1541

How to compute the divisors of 3082?

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 3082 by each of the numbers from 1 to 3082 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)

3082 / 1 = 3082 (the remainder is 0, so 1 is a divisor of 3082)
3082 / 2 = 1541 (the remainder is 0, so 2 is a divisor of 3082)
3082 / 3 = 1027.3333333333 (the remainder is 1, so 3 is not a divisor of 3082)
...
3082 / 3081 = 1.0003245699448 (the remainder is 1, so 3081 is not a divisor of 3082)
3082 / 3082 = 1 (the remainder is 0, so 3082 is a divisor of 3082)

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 3082 (i.e. 55.515763527128). 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 $\frac{N}{d} = D$ )

3082 / 1 = 3082 (the remainder is 0, so 1 and 3082 are divisors of 3082)
3082 / 2 = 1541 (the remainder is 0, so 2 and 1541 are divisors of 3082)
3082 / 3 = 1027.3333333333 (the remainder is 1, so 3 is not a divisor of 3082)
...
3082 / 54 = 57.074074074074 (the remainder is 4, so 54 is not a divisor of 3082)
3082 / 55 = 56.036363636364 (the remainder is 2, so 55 is not a divisor of 3082)