What are the divisors of 1664?

1, 2, 4, 8, 13, 16, 26, 32, 52, 64, 104, 128, 208, 416, 832, 1664

There is a total of 16 positive divisors.
The sum of these divisors is 3570.
The arithmetic mean is 223.125.

14 even divisors

2, 4, 8, 16, 26, 32, 52, 64, 104, 128, 208, 416, 832, 1664

2 odd divisors

1, 13

How to compute the divisors of 1664?

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 1664 by each of the numbers from 1 to 1664 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)

1664 / 1 = 1664 (the remainder is 0, so 1 is a divisor of 1664)
1664 / 2 = 832 (the remainder is 0, so 2 is a divisor of 1664)
1664 / 3 = 554.66666666667 (the remainder is 2, so 3 is not a divisor of 1664)
...
1664 / 1663 = 1.0006013229104 (the remainder is 1, so 1663 is not a divisor of 1664)
1664 / 1664 = 1 (the remainder is 0, so 1664 is a divisor of 1664)

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 1664 (i.e. 40.792156108742). 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 $\frac{N}{d} = D$ )

1664 / 1 = 1664 (the remainder is 0, so 1 and 1664 are divisors of 1664)
1664 / 2 = 832 (the remainder is 0, so 2 and 832 are divisors of 1664)
1664 / 3 = 554.66666666667 (the remainder is 2, so 3 is not a divisor of 1664)
...
1664 / 39 = 42.666666666667 (the remainder is 26, so 39 is not a divisor of 1664)
1664 / 40 = 41.6 (the remainder is 24, so 40 is not a divisor of 1664)