What are the divisors of 6146?

1, 2, 7, 14, 439, 878, 3073, 6146

There is a total of 8 positive divisors.
The sum of these divisors is 10560.
The arithmetic mean is 1320.

4 even divisors

2, 14, 878, 6146

4 odd divisors

1, 7, 439, 3073

How to compute the divisors of 6146?

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 6146 by each of the numbers from 1 to 6146 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)

6146 / 1 = 6146 (the remainder is 0, so 1 is a divisor of 6146)
6146 / 2 = 3073 (the remainder is 0, so 2 is a divisor of 6146)
6146 / 3 = 2048.6666666667 (the remainder is 2, so 3 is not a divisor of 6146)
...
6146 / 6145 = 1.00016273393 (the remainder is 1, so 6145 is not a divisor of 6146)
6146 / 6146 = 1 (the remainder is 0, so 6146 is a divisor of 6146)

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 6146 (i.e. 78.396428490079). 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 $\frac{N}{d} = D$ )

6146 / 1 = 6146 (the remainder is 0, so 1 and 6146 are divisors of 6146)
6146 / 2 = 3073 (the remainder is 0, so 2 and 3073 are divisors of 6146)
6146 / 3 = 2048.6666666667 (the remainder is 2, so 3 is not a divisor of 6146)
...
6146 / 77 = 79.818181818182 (the remainder is 63, so 77 is not a divisor of 6146)
6146 / 78 = 78.794871794872 (the remainder is 62, so 78 is not a divisor of 6146)