What are the divisors of 6016?

1, 2, 4, 8, 16, 32, 47, 64, 94, 128, 188, 376, 752, 1504, 3008, 6016

There is a total of 16 positive divisors.
The sum of these divisors is 12240.
The arithmetic mean is 765.

14 even divisors

2, 4, 8, 16, 32, 64, 94, 128, 188, 376, 752, 1504, 3008, 6016

2 odd divisors

1, 47

How to compute the divisors of 6016?

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 6016 by each of the numbers from 1 to 6016 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)

6016 / 1 = 6016 (the remainder is 0, so 1 is a divisor of 6016)
6016 / 2 = 3008 (the remainder is 0, so 2 is a divisor of 6016)
6016 / 3 = 2005.3333333333 (the remainder is 1, so 3 is not a divisor of 6016)
...
6016 / 6015 = 1.0001662510391 (the remainder is 1, so 6015 is not a divisor of 6016)
6016 / 6016 = 1 (the remainder is 0, so 6016 is a divisor of 6016)

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 6016 (i.e. 77.562877718661). 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 $\frac{N}{d} = D$ )

6016 / 1 = 6016 (the remainder is 0, so 1 and 6016 are divisors of 6016)
6016 / 2 = 3008 (the remainder is 0, so 2 and 3008 are divisors of 6016)
6016 / 3 = 2005.3333333333 (the remainder is 1, so 3 is not a divisor of 6016)
...
6016 / 76 = 79.157894736842 (the remainder is 12, so 76 is not a divisor of 6016)
6016 / 77 = 78.12987012987 (the remainder is 10, so 77 is not a divisor of 6016)