What are the divisors of 6173?

1, 6173

There is a total of 2 positive divisors.
The sum of these divisors is 6174.
The arithmetic mean is 3087.

2 odd divisors

1, 6173

How to compute the divisors of 6173?

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 6173 by each of the numbers from 1 to 6173 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)

6173 / 1 = 6173 (the remainder is 0, so 1 is a divisor of 6173)
6173 / 2 = 3086.5 (the remainder is 1, so 2 is not a divisor of 6173)
6173 / 3 = 2057.6666666667 (the remainder is 2, so 3 is not a divisor of 6173)
...
6173 / 6172 = 1.000162022035 (the remainder is 1, so 6172 is not a divisor of 6173)
6173 / 6173 = 1 (the remainder is 0, so 6173 is a divisor of 6173)

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 6173 (i.e. 78.568441501661). 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 $\frac{N}{d} = D$ )

6173 / 1 = 6173 (the remainder is 0, so 1 and 6173 are divisors of 6173)
6173 / 2 = 3086.5 (the remainder is 1, so 2 is not a divisor of 6173)
6173 / 3 = 2057.6666666667 (the remainder is 2, so 3 is not a divisor of 6173)
...
6173 / 77 = 80.168831168831 (the remainder is 13, so 77 is not a divisor of 6173)
6173 / 78 = 79.141025641026 (the remainder is 11, so 78 is not a divisor of 6173)