What are the divisors of 3200?

1, 2, 4, 5, 8, 10, 16, 20, 25, 32, 40, 50, 64, 80, 100, 128, 160, 200, 320, 400, 640, 800, 1600, 3200

There is a total of 24 positive divisors.
The sum of these divisors is 7905.
The arithmetic mean is 329.375.

21 even divisors

2, 4, 8, 10, 16, 20, 32, 40, 50, 64, 80, 100, 128, 160, 200, 320, 400, 640, 800, 1600, 3200

3 odd divisors

1, 5, 25

How to compute the divisors of 3200?

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 3200 by each of the numbers from 1 to 3200 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)

3200 / 1 = 3200 (the remainder is 0, so 1 is a divisor of 3200)
3200 / 2 = 1600 (the remainder is 0, so 2 is a divisor of 3200)
3200 / 3 = 1066.6666666667 (the remainder is 2, so 3 is not a divisor of 3200)
...
3200 / 3199 = 1.0003125976868 (the remainder is 1, so 3199 is not a divisor of 3200)
3200 / 3200 = 1 (the remainder is 0, so 3200 is a divisor of 3200)

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 3200 (i.e. 56.568542494924). 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 $\frac{N}{d} = D$ )

3200 / 1 = 3200 (the remainder is 0, so 1 and 3200 are divisors of 3200)
3200 / 2 = 1600 (the remainder is 0, so 2 and 1600 are divisors of 3200)
3200 / 3 = 1066.6666666667 (the remainder is 2, so 3 is not a divisor of 3200)
...
3200 / 55 = 58.181818181818 (the remainder is 10, so 55 is not a divisor of 3200)
3200 / 56 = 57.142857142857 (the remainder is 8, so 56 is not a divisor of 3200)