What are the divisors of 3584?

1, 2, 4, 7, 8, 14, 16, 28, 32, 56, 64, 112, 128, 224, 256, 448, 512, 896, 1792, 3584

There is a total of 20 positive divisors.
The sum of these divisors is 8184.
The arithmetic mean is 409.2.

18 even divisors

2, 4, 8, 14, 16, 28, 32, 56, 64, 112, 128, 224, 256, 448, 512, 896, 1792, 3584

2 odd divisors

1, 7

How to compute the divisors of 3584?

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 3584 by each of the numbers from 1 to 3584 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)

3584 / 1 = 3584 (the remainder is 0, so 1 is a divisor of 3584)
3584 / 2 = 1792 (the remainder is 0, so 2 is a divisor of 3584)
3584 / 3 = 1194.6666666667 (the remainder is 2, so 3 is not a divisor of 3584)
...
3584 / 3583 = 1.0002790957298 (the remainder is 1, so 3583 is not a divisor of 3584)
3584 / 3584 = 1 (the remainder is 0, so 3584 is a divisor of 3584)

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 3584 (i.e. 59.866518188383). 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 $\frac{N}{d} = D$ )

3584 / 1 = 3584 (the remainder is 0, so 1 and 3584 are divisors of 3584)
3584 / 2 = 1792 (the remainder is 0, so 2 and 1792 are divisors of 3584)
3584 / 3 = 1194.6666666667 (the remainder is 2, so 3 is not a divisor of 3584)
...
3584 / 58 = 61.793103448276 (the remainder is 46, so 58 is not a divisor of 3584)
3584 / 59 = 60.745762711864 (the remainder is 44, so 59 is not a divisor of 3584)