What are the divisors of 6097?

1, 7, 13, 67, 91, 469, 871, 6097

There is a total of 8 positive divisors.
The sum of these divisors is 7616.
The arithmetic mean is 952.

8 odd divisors

1, 7, 13, 67, 91, 469, 871, 6097

How to compute the divisors of 6097?

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 6097 by each of the numbers from 1 to 6097 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)

6097 / 1 = 6097 (the remainder is 0, so 1 is a divisor of 6097)
6097 / 2 = 3048.5 (the remainder is 1, so 2 is not a divisor of 6097)
6097 / 3 = 2032.3333333333 (the remainder is 1, so 3 is not a divisor of 6097)
...
6097 / 6096 = 1.0001640419948 (the remainder is 1, so 6096 is not a divisor of 6097)
6097 / 6097 = 1 (the remainder is 0, so 6097 is a divisor of 6097)

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 6097 (i.e. 78.08328886516). 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 $\frac{N}{d} = D$ )

6097 / 1 = 6097 (the remainder is 0, so 1 and 6097 are divisors of 6097)
6097 / 2 = 3048.5 (the remainder is 1, so 2 is not a divisor of 6097)
6097 / 3 = 2032.3333333333 (the remainder is 1, so 3 is not a divisor of 6097)
...
6097 / 77 = 79.181818181818 (the remainder is 14, so 77 is not a divisor of 6097)
6097 / 78 = 78.166666666667 (the remainder is 13, so 78 is not a divisor of 6097)