What are the divisors of 6171?

1, 3, 11, 17, 33, 51, 121, 187, 363, 561, 2057, 6171

There is a total of 12 positive divisors.
The sum of these divisors is 9576.
The arithmetic mean is 798.

12 odd divisors

1, 3, 11, 17, 33, 51, 121, 187, 363, 561, 2057, 6171

How to compute the divisors of 6171?

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 6171 by each of the numbers from 1 to 6171 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)

6171 / 1 = 6171 (the remainder is 0, so 1 is a divisor of 6171)
6171 / 2 = 3085.5 (the remainder is 1, so 2 is not a divisor of 6171)
6171 / 3 = 2057 (the remainder is 0, so 3 is a divisor of 6171)
...
6171 / 6170 = 1.0001620745543 (the remainder is 1, so 6170 is not a divisor of 6171)
6171 / 6171 = 1 (the remainder is 0, so 6171 is a divisor of 6171)

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 6171 (i.e. 78.555712713971). 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 $\frac{N}{d} = D$ )

6171 / 1 = 6171 (the remainder is 0, so 1 and 6171 are divisors of 6171)
6171 / 2 = 3085.5 (the remainder is 1, so 2 is not a divisor of 6171)
6171 / 3 = 2057 (the remainder is 0, so 3 and 2057 are divisors of 6171)
...
6171 / 77 = 80.142857142857 (the remainder is 11, so 77 is not a divisor of 6171)
6171 / 78 = 79.115384615385 (the remainder is 9, so 78 is not a divisor of 6171)