ABC26GN0220 · Number System
Subject: General Aptitude · Chapter: Number System · Exam: · Marks: · Difficulty:
What is the number of prime factors contained in the product $30^{7} \times 22^{5} \times 34^{11}$ ?
Answer
Explanation
$$\begin{aligned} (30)^{7} \times(22)^{5} \times(34)^{11} & =(2 \times 3 \times 5)^{7} \times(2 \times 11)^{5} \times(2 \times 17)^{11} \\ & =2^{(7+5+11)} \times 3^{7} \times 5^{7} \times 11^{5} \times 17^{11} \\ & =\left(2^{23} \times 3^{7} \times 5^{7} \times 11^{5} \times 17^{11}\right) . \end{aligned}$$ Number of prime factors $=(23+7+7+5+11)=53$.
Explanation as extracted from the printed page; notation may be imperfect.
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