What are the divisors of 6164?

1, 2, 4, 23, 46, 67, 92, 134, 268, 1541, 3082, 6164

There is a total of 12 positive divisors.
The sum of these divisors is 11424.
The arithmetic mean is 952.

8 even divisors

2, 4, 46, 92, 134, 268, 3082, 6164

4 odd divisors

1, 23, 67, 1541

How to compute the divisors of 6164?

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 6164 by each of the numbers from 1 to 6164 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)

6164 / 1 = 6164 (the remainder is 0, so 1 is a divisor of 6164)
6164 / 2 = 3082 (the remainder is 0, so 2 is a divisor of 6164)
6164 / 3 = 2054.6666666667 (the remainder is 2, so 3 is not a divisor of 6164)
...
6164 / 6163 = 1.0001622586403 (the remainder is 1, so 6163 is not a divisor of 6164)
6164 / 6164 = 1 (the remainder is 0, so 6164 is a divisor of 6164)

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 6164 (i.e. 78.511145705562). 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 $\frac{N}{d} = D$ )

6164 / 1 = 6164 (the remainder is 0, so 1 and 6164 are divisors of 6164)
6164 / 2 = 3082 (the remainder is 0, so 2 and 3082 are divisors of 6164)
6164 / 3 = 2054.6666666667 (the remainder is 2, so 3 is not a divisor of 6164)
...
6164 / 77 = 80.051948051948 (the remainder is 4, so 77 is not a divisor of 6164)
6164 / 78 = 79.025641025641 (the remainder is 2, so 78 is not a divisor of 6164)