performance - How to make this Block of python code short and efficient

Question

I am total newbie to programming and python. I was solving a problem. I found the solution but it seems like too slow.

    if n % 2 == 0 and n % 3 == 0 and
       n % 4 == 0 and n % 5 == 0 and
       n % 6 == 0 and n % 7 == 0 and
       n % 8 == 0 and n % 9 == 0 and
       n % 10 == 0 and n % 11 == 0 and
       n % 12 == 0 and n % 13 == 0 and
       n % 14 == 0 and n % 15 == 0 and
       n % 16 == 0 and n % 17 == 0 and
       n % 18 == 0 and n % 19 == 0 and
       n % 20 == 0:

This is the piece the code to check whether n is divisible by all numbers from 2 to 20 or not.

How I can make it short and efficient.

Answer 1

There's a trade-off between short and efficient.

The Short way is if all(n % i == 0 for i in range(2, 21)):

The Efficient way is to notice that things like n % 20 == 0 also mean that n % f == 0 where f is any factor of 20. For example, you can drop n % 2 == 0. So you'll end up with fewer comparisons which will run faster. In doing this you'll notice a pattern and you'll notice that the entire statement reduces to if n % 232792560 == 0! But that has now deeply embedded the 20 within it so will be difficult to unpick if you need a different upper limit.

So you see that the efficient way is not so easy to read and maintain. So pick the one best suited to your requirements.