What is the greatest positive integer x such that 2x is a factor of 1210?

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问题 What is the greatest positive integer x such that 2^x is a factor of 12¹⁰?

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答案 To reach an answer, you first must find the smallest factors of 12, as follows: 12¹⁰=(3×2×2) ¹⁰ Remember that the exponent applies to every value within the parentheses; thus, (3×2×2) ¹⁰=3¹⁰×2¹⁰×2¹⁰. When multiplying powers with the same base, you add the exponents: 3¹⁰×2^(10+10) =(3¹⁰)(2²⁰); 2²⁰is a factor of 12¹⁰.

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What is the greatest positive integer x such that 2x is a factor of 1210?

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