Question

How many integers from 4 to 50 inclusive are neither multiples of 3 nor 4????

Answer 1

Answer:

24 integers

Step-by-step explanation:

There are (50 - 4)+1 = 47 integers from 4 to 50 INCLUSIVE.

We find the multiples of 3 and find the multiples of 4 and subtract that from the 47 integers to get INTEGERS that are NEITHER multiple of 3 nor 4.

Let's list multiples of 3 (from 4 to 50 inclusive):

6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36, 39, 42, 45, 48

Multiples of 4 (from 4 to 40 inclusive):

4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48

From the 2 lists, let's take out the common ones:

THe common ones are 12, 24, 36, 48

We count all from multiples of 3 list, but don't count the common from multiples of 4's list.

So there are 15 multiples of 3, and 8 multiples of 4

In total 15 + 8 = 23 multiples of 3 and 4

So there are 47 - 23 = 24 integers that are NOT multiples of 3 nor 4