**Question:**

How many numbers are positive divisors of \({2^{10}}{.3^6}{.5^8}\) and divisible by \({2^5}{.3^2}{. 5^4}\)?

**Reference explanation:**

**Correct Answer: GET**

Notice that \({2^{10}}{.3^6}{.5^8} = {2^5}{.3^2}{.5^4}\left( {{2^5) }{{.3}^4}{{.5}^4}} \right)\)

For every positive divisor of \({2^5}{.3^4}{.5^4}\) when multiplied by \({2^{10}}{.3^6}{.5^8} \) are all positive divisors of satisfying the requirements. The number of positive divisors to look for is: \(\left( {5 + 1} \right)\left( {4 + 1} \right)\left( {4 + 1} \right) = 150\).

ADSENSE

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