What are the divisors of 6170?

1, 2, 5, 10, 617, 1234, 3085, 6170

There is a total of 8 positive divisors.
The sum of these divisors is 11124.
The arithmetic mean is 1390.5.

4 even divisors

2, 10, 1234, 6170

4 odd divisors

1, 5, 617, 3085

How to compute the divisors of 6170?

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 6170 by each of the numbers from 1 to 6170 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)

6170 / 1 = 6170 (the remainder is 0, so 1 is a divisor of 6170)
6170 / 2 = 3085 (the remainder is 0, so 2 is a divisor of 6170)
6170 / 3 = 2056.6666666667 (the remainder is 2, so 3 is not a divisor of 6170)
...
6170 / 6169 = 1.0001621008267 (the remainder is 1, so 6169 is not a divisor of 6170)
6170 / 6170 = 1 (the remainder is 0, so 6170 is a divisor of 6170)

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 6170 (i.e. 78.549347546622). 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 $\frac{N}{d} = D$ )

6170 / 1 = 6170 (the remainder is 0, so 1 and 6170 are divisors of 6170)
6170 / 2 = 3085 (the remainder is 0, so 2 and 3085 are divisors of 6170)
6170 / 3 = 2056.6666666667 (the remainder is 2, so 3 is not a divisor of 6170)
...
6170 / 77 = 80.12987012987 (the remainder is 10, so 77 is not a divisor of 6170)
6170 / 78 = 79.102564102564 (the remainder is 8, so 78 is not a divisor of 6170)