Counting numbers divisible by 3 but not by 7
To find out how many numbers from 1 to 200 are divisible by 3 but not by 7, we need to follow these steps:

Step 1: Counting total numbers divisible by 3
- To find the total numbers divisible by 3 from 1 to 200, we can use the formula:
Total numbers = (last number - first number) ÷ divisor + 1
= (200 - 1) ÷ 3 + 1
= 66 + 1
= 67

Step 2: Counting numbers divisible by both 3 and 7
- To find the numbers divisible by both 3 and 7, we need to find the numbers that are divisible by the LCM of 3 and 7, which is 21.
- We need to find the total numbers divisible by 21 from 1 to 200:
Total numbers = (last number - first number) ÷ divisor + 1
= (200 - 1) ÷ 21 + 1
= 9 + 1
= 10

Step 3: Subtracting numbers divisible by both 3 and 7 from total numbers divisible by 3
- Now, we subtract the numbers divisible by both 3 and 7 from the total numbers divisible by 3:
Numbers divisible by 3 but not by 7 = Total numbers divisible by 3 - Total numbers divisible by both 3 and 7
= 67 - 10
= 57
Therefore, there are 57 numbers from 1 to 200 that are divisible by 3 but not by 7.