What are the divisors of 6178?

1, 2, 3089, 6178

There is a total of 4 positive divisors.
The sum of these divisors is 9270.
The arithmetic mean is 2317.5.

2 even divisors

2, 6178

2 odd divisors

1, 3089

How to compute the divisors of 6178?

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 6178 by each of the numbers from 1 to 6178 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)

6178 / 1 = 6178 (the remainder is 0, so 1 is a divisor of 6178)
6178 / 2 = 3089 (the remainder is 0, so 2 is a divisor of 6178)
6178 / 3 = 2059.3333333333 (the remainder is 1, so 3 is not a divisor of 6178)
...
6178 / 6177 = 1.0001618908855 (the remainder is 1, so 6177 is not a divisor of 6178)
6178 / 6178 = 1 (the remainder is 0, so 6178 is a divisor of 6178)

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 6178 (i.e. 78.600254452514). 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 $\frac{N}{d} = D$ )

6178 / 1 = 6178 (the remainder is 0, so 1 and 6178 are divisors of 6178)
6178 / 2 = 3089 (the remainder is 0, so 2 and 3089 are divisors of 6178)
6178 / 3 = 2059.3333333333 (the remainder is 1, so 3 is not a divisor of 6178)
...
6178 / 77 = 80.233766233766 (the remainder is 18, so 77 is not a divisor of 6178)
6178 / 78 = 79.205128205128 (the remainder is 16, so 78 is not a divisor of 6178)