What are the divisors of 6080?

1, 2, 4, 5, 8, 10, 16, 19, 20, 32, 38, 40, 64, 76, 80, 95, 152, 160, 190, 304, 320, 380, 608, 760, 1216, 1520, 3040, 6080

There is a total of 28 positive divisors.
The sum of these divisors is 15240.
The arithmetic mean is 544.28571428571.

24 even divisors

2, 4, 8, 10, 16, 20, 32, 38, 40, 64, 76, 80, 152, 160, 190, 304, 320, 380, 608, 760, 1216, 1520, 3040, 6080

4 odd divisors

1, 5, 19, 95

How to compute the divisors of 6080?

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 6080 by each of the numbers from 1 to 6080 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)

6080 / 1 = 6080 (the remainder is 0, so 1 is a divisor of 6080)
6080 / 2 = 3040 (the remainder is 0, so 2 is a divisor of 6080)
6080 / 3 = 2026.6666666667 (the remainder is 2, so 3 is not a divisor of 6080)
...
6080 / 6079 = 1.0001645007403 (the remainder is 1, so 6079 is not a divisor of 6080)
6080 / 6080 = 1 (the remainder is 0, so 6080 is a divisor of 6080)

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 6080 (i.e. 77.974354758472). 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 $\frac{N}{d} = D$ )

6080 / 1 = 6080 (the remainder is 0, so 1 and 6080 are divisors of 6080)
6080 / 2 = 3040 (the remainder is 0, so 2 and 3040 are divisors of 6080)
6080 / 3 = 2026.6666666667 (the remainder is 2, so 3 is not a divisor of 6080)
...
6080 / 76 = 80 (the remainder is 0, so 76 and 80 are divisors of 6080)
6080 / 77 = 78.961038961039 (the remainder is 74, so 77 is not a divisor of 6080)