How many positive integers less than 2009 are divisible by 28 but not by 12?

Answer 1

To find the positive integers less than 2009 that are divisible by 28 but not by 12, we need to find the multiples of 28 that are not multiples of 12. The least common multiple of 28 and 12 is 84, so we need to find multiples of 28 that are not multiples of 84. Since 28 = 2^2 * 7 and 84 = 2^2 * 3 * 7, the multiples of 28 that are not multiples of 84 are those that have an odd power of 2. The highest multiple of 28 less than 2009 that satisfies this condition is 1976. Therefore, there are 1976 / 28 = 71 positive integers less than 2009 that are divisible by 28 but not by 12.

Answer 2

Oh, dude, so you're asking me to count how many positive integers less than 2009 are divisible by 28 but not by 12? That's like asking me to count how many slices of Pizza I can eat without getting full. Anyway, to answer your question, the answer is 71. Just like how I can probably eat 71 slices of pizza before regretting it.

Answer 3

Well, darling, to find the number of positive integers less than 2009 that are divisible by 28 but not by 12, you need to find the multiples of 28 and then subtract the multiples of 84 (which is the least common multiple of 12 and 28). There are 71 multiples of 28 less than 2009 and 23 multiples of 84. So, the answer is 71 - 23 = 48. Voilà!

Answer 4

48.

Answer 5

48