What are the divisors of 6104?

1, 2, 4, 7, 8, 14, 28, 56, 109, 218, 436, 763, 872, 1526, 3052, 6104

There is a total of 16 positive divisors.
The sum of these divisors is 13200.
The arithmetic mean is 825.

12 even divisors

2, 4, 8, 14, 28, 56, 218, 436, 872, 1526, 3052, 6104

4 odd divisors

1, 7, 109, 763

How to compute the divisors of 6104?

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 6104 by each of the numbers from 1 to 6104 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)

6104 / 1 = 6104 (the remainder is 0, so 1 is a divisor of 6104)
6104 / 2 = 3052 (the remainder is 0, so 2 is a divisor of 6104)
6104 / 3 = 2034.6666666667 (the remainder is 2, so 3 is not a divisor of 6104)
...
6104 / 6103 = 1.0001638538424 (the remainder is 1, so 6103 is not a divisor of 6104)
6104 / 6104 = 1 (the remainder is 0, so 6104 is a divisor of 6104)

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 6104 (i.e. 78.128099938498). 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 $\frac{N}{d} = D$ )

6104 / 1 = 6104 (the remainder is 0, so 1 and 6104 are divisors of 6104)
6104 / 2 = 3052 (the remainder is 0, so 2 and 3052 are divisors of 6104)
6104 / 3 = 2034.6666666667 (the remainder is 2, so 3 is not a divisor of 6104)
...
6104 / 77 = 79.272727272727 (the remainder is 21, so 77 is not a divisor of 6104)
6104 / 78 = 78.25641025641 (the remainder is 20, so 78 is not a divisor of 6104)