How many whole numbers between 1 and 100 can be divided by 2 and 3?

Answer 1

If you mean how many can be divided by both 2 and 3, then it would be the multiples of 6 between 1 and 100: This would be numbers of the form 6k, where k is a whole number. There are 16 values of k for which 1<=6k<=100 [I don't think I can make a proper less than or equal sign on here, so I am using "<="]. k=1,2,3,4,...,16, with 6k=6,12,18,...96

If you mean how many are divisible by either 2 or 3 (or both), this would be the number of whole numbers divisible by 2+the number of whole numbers divisible by 2-the number of whole numbers divisible by 6 [to eliminate double counting]. By the same rationale applied above for 6, there are 50 numbers between 1 and 100 inclusive that can be divided by 2, and 33 numbers that can be divided by 3. So there are are 50+33-15=73 that can be divided by either 2 or 3 (or both).