Quantity A	Quantity B
The number of distinct prime factors of 100,000	The number of distinct prime factors of 99,000

A)The quantity in Column A is greater.
B)The quantity in Column B is greater.
C)The two quantities are equal.
D)The relationship cannot be determined from the information given.
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Sandy
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Explanation

Since only the number of distinct prime factors matter, not what they are or how many times they are present, it is possible to tell on sight that Quantity A has only 2 distinct prime factors, because 100,000 is a power of 10. (Any prime tree for 10, 100, or 1,000, etc. will contain only the prime factors 2 and 5, occurring in pairs.)

In Quantity B, 99,000 breaks down as 99 × 1,000. Since 1,000 also contains 2’s and 5’s, and 99 contains even more factors (specifically 3, 3, and 11), Quantity B is greater. It is not necessary to make prime factor trees for each number.
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Sandy
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