How many integers between 10 and 60, inclusive, can be evenly divided by neither 2 nor 3?

Find total number of integers.



Find how many integers is divisible by 2.



Eliminate even numbers.

11, 13, 15,..., 57, 59

This array contains 51 - 26 = 25 numbers.

Eliminate numbers before the first number divisible by 3 and after the last number divisible by 3.

15, 17, 19,..., 55, 57

This array contains 25 - 3 = 22 numbers.

Now we should eliminate numbers divisible by 3: 15, 21, 27...



There are 8 such numbers.

Therefore, there are 25 - 8 = 17 numbers that can be evenly divided by neither 2 nor 3