What are the divisors of 6133?

1, 6133

There is a total of 2 positive divisors.
The sum of these divisors is 6134.
The arithmetic mean is 3067.

2 odd divisors

1, 6133

How to compute the divisors of 6133?

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 6133 by each of the numbers from 1 to 6133 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)

6133 / 1 = 6133 (the remainder is 0, so 1 is a divisor of 6133)
6133 / 2 = 3066.5 (the remainder is 1, so 2 is not a divisor of 6133)
6133 / 3 = 2044.3333333333 (the remainder is 1, so 3 is not a divisor of 6133)
...
6133 / 6132 = 1.0001630789302 (the remainder is 1, so 6132 is not a divisor of 6133)
6133 / 6133 = 1 (the remainder is 0, so 6133 is a divisor of 6133)

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 6133 (i.e. 78.313472659562). 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 $\frac{N}{d} = D$ )

6133 / 1 = 6133 (the remainder is 0, so 1 and 6133 are divisors of 6133)
6133 / 2 = 3066.5 (the remainder is 1, so 2 is not a divisor of 6133)
6133 / 3 = 2044.3333333333 (the remainder is 1, so 3 is not a divisor of 6133)
...
6133 / 77 = 79.649350649351 (the remainder is 50, so 77 is not a divisor of 6133)
6133 / 78 = 78.628205128205 (the remainder is 49, so 78 is not a divisor of 6133)