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Answered 2010-11-25 05:43:20

In order to be divisible by both 2 and 3, a number must be divisible by 6.

The largest multiple of 6 less than 100 is 96 ... the 16th multiple of 6.

So there are 16 of them.

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There are 75 whole numbers from 100 to 999 that are divisible by both three and four.


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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).





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