What are the divisors of 5600?

1, 2, 4, 5, 7, 8, 10, 14, 16, 20, 25, 28, 32, 35, 40, 50, 56, 70, 80, 100, 112, 140, 160, 175, 200, 224, 280, 350, 400, 560, 700, 800, 1120, 1400, 2800, 5600

There is a total of 36 positive divisors.
The sum of these divisors is 15624.
The arithmetic mean is 434.

30 even divisors

2, 4, 8, 10, 14, 16, 20, 28, 32, 40, 50, 56, 70, 80, 100, 112, 140, 160, 200, 224, 280, 350, 400, 560, 700, 800, 1120, 1400, 2800, 5600

6 odd divisors

1, 5, 7, 25, 35, 175

How to compute the divisors of 5600?

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 5600 by each of the numbers from 1 to 5600 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)

5600 / 1 = 5600 (the remainder is 0, so 1 is a divisor of 5600)
5600 / 2 = 2800 (the remainder is 0, so 2 is a divisor of 5600)
5600 / 3 = 1866.6666666667 (the remainder is 2, so 3 is not a divisor of 5600)
...
5600 / 5599 = 1.000178603322 (the remainder is 1, so 5599 is not a divisor of 5600)
5600 / 5600 = 1 (the remainder is 0, so 5600 is a divisor of 5600)

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 5600 (i.e. 74.833147735479). 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 $\frac{N}{d} = D$ )

5600 / 1 = 5600 (the remainder is 0, so 1 and 5600 are divisors of 5600)
5600 / 2 = 2800 (the remainder is 0, so 2 and 2800 are divisors of 5600)
5600 / 3 = 1866.6666666667 (the remainder is 2, so 3 is not a divisor of 5600)
...
5600 / 73 = 76.712328767123 (the remainder is 52, so 73 is not a divisor of 5600)
5600 / 74 = 75.675675675676 (the remainder is 50, so 74 is not a divisor of 5600)