What are the divisors of 6176?

1, 2, 4, 8, 16, 32, 193, 386, 772, 1544, 3088, 6176

There is a total of 12 positive divisors.
The sum of these divisors is 12222.
The arithmetic mean is 1018.5.

10 even divisors

2, 4, 8, 16, 32, 386, 772, 1544, 3088, 6176

2 odd divisors

1, 193

How to compute the divisors of 6176?

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 6176 by each of the numbers from 1 to 6176 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)

6176 / 1 = 6176 (the remainder is 0, so 1 is a divisor of 6176)
6176 / 2 = 3088 (the remainder is 0, so 2 is a divisor of 6176)
6176 / 3 = 2058.6666666667 (the remainder is 2, so 3 is not a divisor of 6176)
...
6176 / 6175 = 1.0001619433198 (the remainder is 1, so 6175 is not a divisor of 6176)
6176 / 6176 = 1 (the remainder is 0, so 6176 is a divisor of 6176)

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 6176 (i.e. 78.587530817554). 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 $\frac{N}{d} = D$ )

6176 / 1 = 6176 (the remainder is 0, so 1 and 6176 are divisors of 6176)
6176 / 2 = 3088 (the remainder is 0, so 2 and 3088 are divisors of 6176)
6176 / 3 = 2058.6666666667 (the remainder is 2, so 3 is not a divisor of 6176)
...
6176 / 77 = 80.207792207792 (the remainder is 16, so 77 is not a divisor of 6176)
6176 / 78 = 79.179487179487 (the remainder is 14, so 78 is not a divisor of 6176)