The Number of Prime Factors of (6)^10 x(7)^17x(55)^27 is GMAT Problem Solving

Question: The number of prime factors of (6)^10x(7)^17x(55)^27 is

1. 54
2. 64
3. 81
4. 91

“The number of prime factors of (6)^10 x(7)^17x(55)^27 is" - is a topic of the GMAT Quantitative reasoning section of GMAT. This question has been borrowed from the book “GMAT Official Guide Quantitative Review”.

To understand GMAT Problem Solving questions, applicants must possess fundamental qualitative skills. Quant tests a candidate's aptitude in reasoning and mathematics. The GMAT Quantitative test's problem-solving phase consists of a question and a list of possible responses. By using mathematics to answer the question, the candidate must select the appropriate response. The problem-solving section of the GMAT Quant topic is made up of very complicated math problems that must be solved by using the right math facts.

Answer: D
Solution and Explanation:
Approach Solution 1:

It has asked to find out the prime factors of the given expression
(6)^10∗(7)^17∗(55)^27
Factoring the inside terms,

(2∗3)^10∗(7)^17∗(5∗11)^27
2^10∗3^10∗7^17∗5^27∗11^27
Note: (x∗y)^k=x^k∗y^k

We have to add the powers to get the number of prime factors.
10+10+17+27+27=91
It has 91 prime factors
D is the correct answer.

Correct Answer: D

Approach Solution 2:

It has asked to find out the prime factors of the given expression
(6)^10∗(7)^17∗(55)^2

6^10= (2x3)^10
In this expansion of the exponent,
2 appearing 10 times, 3 appearing 10 times
Total = 20
7^17= 7 is appearing 17 times
55^27= (5x11)^27- 5 is appearing 27 times, 11 appearing 27 times

Total- 20+17+27+27= 91
D is the correct answer.

Correct Answer: D

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