What are the divisors of 6167?

1, 7, 881, 6167

There is a total of 4 positive divisors.
The sum of these divisors is 7056.
The arithmetic mean is 1764.

4 odd divisors

1, 7, 881, 6167

How to compute the divisors of 6167?

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 6167 by each of the numbers from 1 to 6167 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)

6167 / 1 = 6167 (the remainder is 0, so 1 is a divisor of 6167)
6167 / 2 = 3083.5 (the remainder is 1, so 2 is not a divisor of 6167)
6167 / 3 = 2055.6666666667 (the remainder is 2, so 3 is not a divisor of 6167)
...
6167 / 6166 = 1.0001621796951 (the remainder is 1, so 6166 is not a divisor of 6167)
6167 / 6167 = 1 (the remainder is 0, so 6167 is a divisor of 6167)

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 6167 (i.e. 78.530248949051). 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 $\frac{N}{d} = D$ )

6167 / 1 = 6167 (the remainder is 0, so 1 and 6167 are divisors of 6167)
6167 / 2 = 3083.5 (the remainder is 1, so 2 is not a divisor of 6167)
6167 / 3 = 2055.6666666667 (the remainder is 2, so 3 is not a divisor of 6167)
...
6167 / 77 = 80.090909090909 (the remainder is 7, so 77 is not a divisor of 6167)
6167 / 78 = 79.064102564103 (the remainder is 5, so 78 is not a divisor of 6167)