What are the divisors of 6064?

1, 2, 4, 8, 16, 379, 758, 1516, 3032, 6064

There is a total of 10 positive divisors.
The sum of these divisors is 11780.
The arithmetic mean is 1178.

8 even divisors

2, 4, 8, 16, 758, 1516, 3032, 6064

2 odd divisors

1, 379

How to compute the divisors of 6064?

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 6064 by each of the numbers from 1 to 6064 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)

6064 / 1 = 6064 (the remainder is 0, so 1 is a divisor of 6064)
6064 / 2 = 3032 (the remainder is 0, so 2 is a divisor of 6064)
6064 / 3 = 2021.3333333333 (the remainder is 1, so 3 is not a divisor of 6064)
...
6064 / 6063 = 1.0001649348507 (the remainder is 1, so 6063 is not a divisor of 6064)
6064 / 6064 = 1 (the remainder is 0, so 6064 is a divisor of 6064)

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 6064 (i.e. 77.871689335727). 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 $\frac{N}{d} = D$ )

6064 / 1 = 6064 (the remainder is 0, so 1 and 6064 are divisors of 6064)
6064 / 2 = 3032 (the remainder is 0, so 2 and 3032 are divisors of 6064)
6064 / 3 = 2021.3333333333 (the remainder is 1, so 3 is not a divisor of 6064)
...
6064 / 76 = 79.789473684211 (the remainder is 60, so 76 is not a divisor of 6064)
6064 / 77 = 78.753246753247 (the remainder is 58, so 77 is not a divisor of 6064)