What are the divisors of 6134?

1, 2, 3067, 6134

There is a total of 4 positive divisors.
The sum of these divisors is 9204.
The arithmetic mean is 2301.

2 even divisors

2, 6134

2 odd divisors

1, 3067

How to compute the divisors of 6134?

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 6134 by each of the numbers from 1 to 6134 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)

6134 / 1 = 6134 (the remainder is 0, so 1 is a divisor of 6134)
6134 / 2 = 3067 (the remainder is 0, so 2 is a divisor of 6134)
6134 / 3 = 2044.6666666667 (the remainder is 2, so 3 is not a divisor of 6134)
...
6134 / 6133 = 1.0001630523398 (the remainder is 1, so 6133 is not a divisor of 6134)
6134 / 6134 = 1 (the remainder is 0, so 6134 is a divisor of 6134)

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 6134 (i.e. 78.319856996805). 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 $\frac{N}{d} = D$ )

6134 / 1 = 6134 (the remainder is 0, so 1 and 6134 are divisors of 6134)
6134 / 2 = 3067 (the remainder is 0, so 2 and 3067 are divisors of 6134)
6134 / 3 = 2044.6666666667 (the remainder is 2, so 3 is not a divisor of 6134)
...
6134 / 77 = 79.662337662338 (the remainder is 51, so 77 is not a divisor of 6134)
6134 / 78 = 78.641025641026 (the remainder is 50, so 78 is not a divisor of 6134)