What are the divisors of 6130?

1, 2, 5, 10, 613, 1226, 3065, 6130

There is a total of 8 positive divisors.
The sum of these divisors is 11052.
The arithmetic mean is 1381.5.

4 even divisors

2, 10, 1226, 6130

4 odd divisors

1, 5, 613, 3065

How to compute the divisors of 6130?

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 6130 by each of the numbers from 1 to 6130 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)

6130 / 1 = 6130 (the remainder is 0, so 1 is a divisor of 6130)
6130 / 2 = 3065 (the remainder is 0, so 2 is a divisor of 6130)
6130 / 3 = 2043.3333333333 (the remainder is 1, so 3 is not a divisor of 6130)
...
6130 / 6129 = 1.0001631587535 (the remainder is 1, so 6129 is not a divisor of 6130)
6130 / 6130 = 1 (the remainder is 0, so 6130 is a divisor of 6130)

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 6130 (i.e. 78.294316524254). 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 $\frac{N}{d} = D$ )

6130 / 1 = 6130 (the remainder is 0, so 1 and 6130 are divisors of 6130)
6130 / 2 = 3065 (the remainder is 0, so 2 and 3065 are divisors of 6130)
6130 / 3 = 2043.3333333333 (the remainder is 1, so 3 is not a divisor of 6130)
...
6130 / 77 = 79.61038961039 (the remainder is 47, so 77 is not a divisor of 6130)
6130 / 78 = 78.589743589744 (the remainder is 46, so 78 is not a divisor of 6130)