Two, Three, but not SixPro 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?
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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?
The least common multiple of x and 36 is 180. The greatest common factor of x and 36 is 4. What is the value of x?
How many integers between 1 and 1000 inclusive are multiples of either 2 or 3?
Reduce the following number to its prime factorization, without use of a calculator: 1006005. Explain the steps in your process.
x has 2n - 9 more divisors than x - 4, and it has 2n - 7 divisors more than x + 5.
What are the possible values of n, if x is a positive integer less than 50?
What number is missing from the following list?
1, 2, 3, 4, 6, 8, 9, 18, 24, 36, 72
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