What are the divisors of 6182?

1, 2, 11, 22, 281, 562, 3091, 6182

There is a total of 8 positive divisors.
The sum of these divisors is 10152.
The arithmetic mean is 1269.

4 even divisors

2, 22, 562, 6182

4 odd divisors

1, 11, 281, 3091

How to compute the divisors of 6182?

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 6182 by each of the numbers from 1 to 6182 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)

6182 / 1 = 6182 (the remainder is 0, so 1 is a divisor of 6182)
6182 / 2 = 3091 (the remainder is 0, so 2 is a divisor of 6182)
6182 / 3 = 2060.6666666667 (the remainder is 2, so 3 is not a divisor of 6182)
...
6182 / 6181 = 1.0001617861188 (the remainder is 1, so 6181 is not a divisor of 6182)
6182 / 6182 = 1 (the remainder is 0, so 6182 is a divisor of 6182)

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 6182 (i.e. 78.625695545413). 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 $\frac{N}{d} = D$ )

6182 / 1 = 6182 (the remainder is 0, so 1 and 6182 are divisors of 6182)
6182 / 2 = 3091 (the remainder is 0, so 2 and 3091 are divisors of 6182)
6182 / 3 = 2060.6666666667 (the remainder is 2, so 3 is not a divisor of 6182)
...
6182 / 77 = 80.285714285714 (the remainder is 22, so 77 is not a divisor of 6182)
6182 / 78 = 79.25641025641 (the remainder is 20, so 78 is not a divisor of 6182)