The number of positive integers that are less than 500 and that are not divisable by 2 or 3 is?
There are 250 divisible by 2, 166 divisible by 3 and 83 divisible by both. So 250 + 166 - 83 = the numbers divisible by 2 or 3, without double counting. Subtract that number from 500.
How did you get 83?
That's the number of positive integers less than 500 divisible by 2 and 3. If you don't subtract that number out, then you'll double count them since they are already included in the counts of both multiples of 2 and 3.
To get the number of positive integers that are less than 500 and not divisible by 2 or 3, we need to subtract the number of positive integers divisible by 2 or 3 from 500.
To find these counts, we can use the principle of inclusion-exclusion.
There are 250 positive integers less than 500 that are divisible by 2. This is because we can find the number of multiples of 2 less than 500 by dividing 500 by 2 (since multiples of 2 are evenly spaced) which gives us 250.
Similarly, there are 166 positive integers less than 500 that are divisible by 3. This is because we can find the number of multiples of 3 less than 500 by dividing 500 by 3 (since multiples of 3 are also evenly spaced) which gives us 166.
But, when counting the multiples of 2 and 3, we will be double counting the integers that are divisible by both 2 and 3. To correct for this, we need to subtract the number of positive integers that are divisible by both 2 and 3, which is 83.
Therefore, the number of positive integers that are less than 500 and not divisible by 2 or 3 can be calculated as follows:
Total = 500 - (250 + 166 - 83)
Simplifying the expression inside the parentheses:
Total = 500 - 333
So the final answer is:
Total = 167
There are 167 positive integers less than 500 that are not divisible by 2 or 3.