Question : The total number of prime factors in $4^{10}\times 7^{3}\times 16^{2}\times11\times 10^{2}$ is:
Option 1: 34
Option 2: 35
Option 3: 36
Option 4: 37
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Correct Answer: 36
Solution :
Given:
$4^{10}\times7^{3}\times16^{2}\times11\times10^{2}$
Rewrite this equation with the prime factors.
$(2^{2})^{10}\times7^{3}\times(2^{4})^{2}\times11\times2^{2}\times5^{2}$
= $2^{20+8+2}\times7^{3}\times11^{1}\times5^{2}$
= $2^{30}\times7^{3}\times11^{1}\times5^{2}$
Total number of prime factors = 30 + 3 + 1 + 2 = 36
Hence, the correct answer is 36.
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