What are the divisors of 6179?

1, 37, 167, 6179

There is a total of 4 positive divisors.
The sum of these divisors is 6384.
The arithmetic mean is 1596.

4 odd divisors

1, 37, 167, 6179

How to compute the divisors of 6179?

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 6179 by each of the numbers from 1 to 6179 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)

6179 / 1 = 6179 (the remainder is 0, so 1 is a divisor of 6179)
6179 / 2 = 3089.5 (the remainder is 1, so 2 is not a divisor of 6179)
6179 / 3 = 2059.6666666667 (the remainder is 2, so 3 is not a divisor of 6179)
...
6179 / 6178 = 1.0001618646811 (the remainder is 1, so 6178 is not a divisor of 6179)
6179 / 6179 = 1 (the remainder is 0, so 6179 is a divisor of 6179)

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 6179 (i.e. 78.606615497679). 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 $\frac{N}{d} = D$ )

6179 / 1 = 6179 (the remainder is 0, so 1 and 6179 are divisors of 6179)
6179 / 2 = 3089.5 (the remainder is 1, so 2 is not a divisor of 6179)
6179 / 3 = 2059.6666666667 (the remainder is 2, so 3 is not a divisor of 6179)
...
6179 / 77 = 80.246753246753 (the remainder is 19, so 77 is not a divisor of 6179)
6179 / 78 = 79.217948717949 (the remainder is 17, so 78 is not a divisor of 6179)