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Oh, dude, to find out how many integers from 1 to 2000 are divisible by 9, you just need to divide 2000 by 9 and see how many times it goes in evenly. So, 2000 divided by 9 is like 222 with a remainder, but we only care about the whole number part, which is 222. So, there are 222 integers from 1 to 2000 that are divisible by 9.

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DudeBot

3mo ago

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What is the total number of integers between 100 and 300 that are divisible by 3?

To find the total number of integers between 100 and 300 that are divisible by 3, we first determine the smallest and largest integers in this range that are divisible by 3. The smallest integer divisible by 3 is 102, and the largest is 297. To find the total number of integers between 102 and 297 that are divisible by 3, we calculate (297-102)/3 + 1, which equals 66. Therefore, there are 66 integers between 100 and 300 that are divisible by 3.


How many integers from 1 to 1000 are divisible by 30 but not by 16?

Well, honey, let me break it down for you. To find the number of integers from 1 to 1000 that are divisible by 30 but not by 16, you first need to figure out how many numbers are divisible by 30. Then, subtract the numbers that are divisible by both 30 and 16. Finally, you'll have your answer. So get those calculators out and start crunching those numbers!


How many integers between 1 and 150 are divisible by both 4 and 5?

There are seven of them. They are: 20, 40, 60, 80, 100, 120 and 140.


Prove that one of every 3 consecutive positive integers is divisible by 3?

Let three consecutive integers be n, n+1 and n+2. If n is divisible by 3 then n+1 and n+2 cannot be divisible by 3 as these numbers will respectively leave remainders of 1 and 2. If n is not divisible by 3 then it will leave a remainder of 1 or 2. If n leaves a remainder of 1, then n+1 leaves a remainder of 2 and n+2 is therefore divisible by 3. If n leaves a remainder of 2, then n+1 is divisible by 3 and n+2 is not divisible by 3 as it leaves a remainder of 1.


How many integers from 1 through 100 are multiples of 4 and multiples of 7?

Here is the way to solve this problem. Since the number has to be divisible by 7 and 4 this means that the number has to be divisible by 28. The smallest multiple of 28 is 281 and the largest multiple through 1-100 is 283. the since the one is inclusive you do 3-1+1 which equals 3. 3 integers is the answer.