How many numbers are there from 1 to 200 which are exactly divisible by 21 but not by 7?

Question

Answer

Counting numbers divisible by 21 but not by 7 from 1 to 200

Finding the multiples of 21: To find the numbers divisible by 21, we need to find the multiples of 21 from 1 to 200. The first multiple of 21 is 21 itself, and the last multiple of 21 that is less than or equal to 200 is 189. We can find this by dividing 200 by 21 and taking the floor of the result (i.e. the largest integer less than or equal to the result): floor(200/21) = 9.

Finding the multiples of 7: To ensure that the numbers we count are not divisible by 7, we need to exclude the multiples of 7 from our list of multiples of 21. The first multiple of 7 is 7, and the last multiple of 7 that is less than or equal to 189 is 182. We can find this by dividing 189 by 7 and taking the floor of the result: floor(189/7) = 27.

Finding the numbers divisible by 21 but not by 7: To find the numbers that are divisible by 21 but not by 7, we need to subtract the number of multiples of 21 that are also multiples of 7 from the total number of multiples of 21. We found that there are 9 multiples of 21, and 27 multiples of 7. Therefore, the number of numbers divisible by 21 but not by 7 is 9 - 27 = -18. However, this result does not make sense, as we cannot have negative numbers of counted numbers. Therefore, there are no numbers from 1 to 200 that are divisible by 21 but not by 7.