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How many positive integers are less then 50?
49
How many positive integers less than 1000 are not divisible by 3?
666 integers.
How many positive integers less than 2010 have an odd number of factors?
There are 44 positive integers less than 2,010 that have an odd number of factors.
How many positive integers less than 1000 are divisible by 7 and are not divisible by 11?
There are 130 positive integers less than 1,000 that are divisible by seven but not divisible by 11
How many positive integers less than 1000 are either divisible by 2 or by 11?
There are 544 positive integers less than 1,000 that are either divisible by two or by 11.
How many positive integers less than or equal to 100 have a prime factor that is greater than 4?
There are 80 such integers.
How many positive integers are less then 50?
49
How many positive integers less than 1000 are not divisible by 3?
666 integers.
How many positive integers less than 2010 have an odd number of factors?
There are 44 positive integers less than 2,010 that have an odd number of factors.
How many positive integers less than 1000 are divisible by 7 and are not divisible by 11?
There are 130 positive integers less than 1,000 that are divisible by seven but not divisible by 11
How many positive integers less than 1000 are either divisible by 2 or by 11?
There are 544 positive integers less than 1,000 that are either divisible by two or by 11.
How many positive integers less than 20 are prime?
Eight.
How many positive integers less than 200 are divisible by 2 3 5?
6
How many positive integers are there less than 10000?
One less than 10000.
How many positive integers less than 100 have an odd number of positive divisors?
The squares -- nine of them.
How many elements are there in the set of positive integers less than 8?
7 of them.
How many positive integers less than 2008 have an even number of divisors?
There are 1,963 such integers. Every factor of a number has a pair. The only time there will be an odd number of factors is if one factor is repeated, ie the number is a perfect square. So the question is really asking: how many positive integers less than 2008 (in the range 1 to 2007) are not perfect squares. √2007 = 44 and a bit (it lies between 44 and 45) So there are 44 integers less than (or equal to) 2007 which are perfect squares → 2007 - 44 = 1963 integers are not perfect squares in the range 1-2007 and have an even number of factors (divisors).
