What are the divisors of 7050?

1, 2, 3, 5, 6, 10, 15, 25, 30, 47, 50, 75, 94, 141, 150, 235, 282, 470, 705, 1175, 1410, 2350, 3525, 7050

There is a total of 24 positive divisors.
The sum of these divisors is 17856.
The arithmetic mean is 744.

12 even divisors

2, 6, 10, 30, 50, 94, 150, 282, 470, 1410, 2350, 7050

12 odd divisors

1, 3, 5, 15, 25, 47, 75, 141, 235, 705, 1175, 3525

How to compute the divisors of 7050?

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 7050 by each of the numbers from 1 to 7050 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)

7050 / 1 = 7050 (the remainder is 0, so 1 is a divisor of 7050)
7050 / 2 = 3525 (the remainder is 0, so 2 is a divisor of 7050)
7050 / 3 = 2350 (the remainder is 0, so 3 is a divisor of 7050)
...
7050 / 7049 = 1.0001418640942 (the remainder is 1, so 7049 is not a divisor of 7050)
7050 / 7050 = 1 (the remainder is 0, so 7050 is a divisor of 7050)

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 7050 (i.e. 83.964278118733). 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 $\frac{N}{d} = D$ )

7050 / 1 = 7050 (the remainder is 0, so 1 and 7050 are divisors of 7050)
7050 / 2 = 3525 (the remainder is 0, so 2 and 3525 are divisors of 7050)
7050 / 3 = 2350 (the remainder is 0, so 3 and 2350 are divisors of 7050)
...
7050 / 82 = 85.975609756098 (the remainder is 80, so 82 is not a divisor of 7050)
7050 / 83 = 84.939759036145 (the remainder is 78, so 83 is not a divisor of 7050)