# Two, Three, but not Six

Pro Problems > Math > Number and Quantity > Number Theory > Divisors## Two, Three, but not Six

How many integers between 1 and 100 inclusive are multiples of either 2 or 3, but not of 6?

## Solution

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### GCF and LCM

The greatest common factor of two positive integers is 12, and their least common multiple is 72. If the sum of the numbers is less than 72, what are the numbers?

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What are the possible values of n, if x is a positive integer less than 50?

### No-Calculator Factoring

Reduce the following number to its prime factorization, without use of a calculator: 1006005. Explain the steps in your process.

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### Find the Missing Number

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### Multiples of Two and Three

How many integers between 1 and 1000 inclusive are multiples of either 2 or 3?

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