What are the divisors of 2064?

1, 2, 3, 4, 6, 8, 12, 16, 24, 43, 48, 86, 129, 172, 258, 344, 516, 688, 1032, 2064

There is a total of 20 positive divisors.
The sum of these divisors is 5456.
The arithmetic mean is 272.8.

16 even divisors

2, 4, 6, 8, 12, 16, 24, 48, 86, 172, 258, 344, 516, 688, 1032, 2064

4 odd divisors

1, 3, 43, 129

How to compute the divisors of 2064?

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 2064 by each of the numbers from 1 to 2064 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)

2064 / 1 = 2064 (the remainder is 0, so 1 is a divisor of 2064)
2064 / 2 = 1032 (the remainder is 0, so 2 is a divisor of 2064)
2064 / 3 = 688 (the remainder is 0, so 3 is a divisor of 2064)
...
2064 / 2063 = 1.0004847309743 (the remainder is 1, so 2063 is not a divisor of 2064)
2064 / 2064 = 1 (the remainder is 0, so 2064 is a divisor of 2064)

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 2064 (i.e. 45.431266766402). 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 $\frac{N}{d} = D$ )

2064 / 1 = 2064 (the remainder is 0, so 1 and 2064 are divisors of 2064)
2064 / 2 = 1032 (the remainder is 0, so 2 and 1032 are divisors of 2064)
2064 / 3 = 688 (the remainder is 0, so 3 and 688 are divisors of 2064)
...
2064 / 44 = 46.909090909091 (the remainder is 40, so 44 is not a divisor of 2064)
2064 / 45 = 45.866666666667 (the remainder is 39, so 45 is not a divisor of 2064)