What are the divisors of 4064?

1, 2, 4, 8, 16, 32, 127, 254, 508, 1016, 2032, 4064

There is a total of 12 positive divisors.
The sum of these divisors is 8064.
The arithmetic mean is 672.

10 even divisors

2, 4, 8, 16, 32, 254, 508, 1016, 2032, 4064

2 odd divisors

1, 127

How to compute the divisors of 4064?

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 4064 by each of the numbers from 1 to 4064 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)

4064 / 1 = 4064 (the remainder is 0, so 1 is a divisor of 4064)
4064 / 2 = 2032 (the remainder is 0, so 2 is a divisor of 4064)
4064 / 3 = 1354.6666666667 (the remainder is 2, so 3 is not a divisor of 4064)
...
4064 / 4063 = 1.000246123554 (the remainder is 1, so 4063 is not a divisor of 4064)
4064 / 4064 = 1 (the remainder is 0, so 4064 is a divisor of 4064)

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 4064 (i.e. 63.749509802037). 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 $\frac{N}{d} = D$ )

4064 / 1 = 4064 (the remainder is 0, so 1 and 4064 are divisors of 4064)
4064 / 2 = 2032 (the remainder is 0, so 2 and 2032 are divisors of 4064)
4064 / 3 = 1354.6666666667 (the remainder is 2, so 3 is not a divisor of 4064)
...
4064 / 62 = 65.548387096774 (the remainder is 34, so 62 is not a divisor of 4064)
4064 / 63 = 64.507936507937 (the remainder is 32, so 63 is not a divisor of 4064)