What are the divisors of 5700?

1, 2, 3, 4, 5, 6, 10, 12, 15, 19, 20, 25, 30, 38, 50, 57, 60, 75, 76, 95, 100, 114, 150, 190, 228, 285, 300, 380, 475, 570, 950, 1140, 1425, 1900, 2850, 5700

There is a total of 36 positive divisors.
The sum of these divisors is 17360.
The arithmetic mean is 482.22222222222.

24 even divisors

2, 4, 6, 10, 12, 20, 30, 38, 50, 60, 76, 100, 114, 150, 190, 228, 300, 380, 570, 950, 1140, 1900, 2850, 5700

12 odd divisors

1, 3, 5, 15, 19, 25, 57, 75, 95, 285, 475, 1425

How to compute the divisors of 5700?

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 5700 by each of the numbers from 1 to 5700 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)

5700 / 1 = 5700 (the remainder is 0, so 1 is a divisor of 5700)
5700 / 2 = 2850 (the remainder is 0, so 2 is a divisor of 5700)
5700 / 3 = 1900 (the remainder is 0, so 3 is a divisor of 5700)
...
5700 / 5699 = 1.0001754693806 (the remainder is 1, so 5699 is not a divisor of 5700)
5700 / 5700 = 1 (the remainder is 0, so 5700 is a divisor of 5700)

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 5700 (i.e. 75.498344352707). 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 $\frac{N}{d} = D$ )

5700 / 1 = 5700 (the remainder is 0, so 1 and 5700 are divisors of 5700)
5700 / 2 = 2850 (the remainder is 0, so 2 and 2850 are divisors of 5700)
5700 / 3 = 1900 (the remainder is 0, so 3 and 1900 are divisors of 5700)
...
5700 / 74 = 77.027027027027 (the remainder is 2, so 74 is not a divisor of 5700)
5700 / 75 = 76 (the remainder is 0, so 75 and 76 are divisors of 5700)