What are the divisors of 6137?

1, 17, 19, 323, 361, 6137

There is a total of 6 positive divisors.
The sum of these divisors is 6858.
The arithmetic mean is 1143.

6 odd divisors

1, 17, 19, 323, 361, 6137

How to compute the divisors of 6137?

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 6137 by each of the numbers from 1 to 6137 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)

6137 / 1 = 6137 (the remainder is 0, so 1 is a divisor of 6137)
6137 / 2 = 3068.5 (the remainder is 1, so 2 is not a divisor of 6137)
6137 / 3 = 2045.6666666667 (the remainder is 2, so 3 is not a divisor of 6137)
...
6137 / 6136 = 1.0001629726206 (the remainder is 1, so 6136 is not a divisor of 6137)
6137 / 6137 = 1 (the remainder is 0, so 6137 is a divisor of 6137)

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 6137 (i.e. 78.339006886736). 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 $\frac{N}{d} = D$ )

6137 / 1 = 6137 (the remainder is 0, so 1 and 6137 are divisors of 6137)
6137 / 2 = 3068.5 (the remainder is 1, so 2 is not a divisor of 6137)
6137 / 3 = 2045.6666666667 (the remainder is 2, so 3 is not a divisor of 6137)
...
6137 / 77 = 79.701298701299 (the remainder is 54, so 77 is not a divisor of 6137)
6137 / 78 = 78.679487179487 (the remainder is 53, so 78 is not a divisor of 6137)