## Que: How many different prime factors of $$4^5+4^6+4^7$$ are there?

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### Que: How many different prime factors of $$4^5+4^6+4^7$$ are there?

by [email protected] Revolution » Mon May 10, 2021 9:26 pm

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Que: How many different prime factors of $$4^5+4^6+4^7$$ are there?

A. 2
B. 3
C. 1
D. 5
E. 6 Math Revolution

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[Course] Starting $79 for on-demand and$60 for tutoring per hour and $390 only for Live Online. Email to : [email protected] Elite Legendary Member Posts: 3906 Joined: 24 Jul 2015 Location: Las Vegas, USA Thanked: 19 times Followed by:36 members ### Re: Que: How many different prime factors of $$4^5+4^6+4^7$$ are there? by [email protected] Revolution » Thu May 13, 2021 9:24 pm Solution: Factors of M are the integers dividing M without a remainder => If M=ab (a and b are positive integers) => a and b are factors of M => When M is expressed as a product of its prime factors only => We have prime factorized M =>If we prime factorize a positive integer M => M = $$\left(p_1\right)^{t_1}\ \ \ \cdot\ \ \left(p_2\right)^{t_2}\ \ \ ......\ \left(p_n\right)^{t_n}$$ => $$p_i$$: Different prime factors and $$t_i$$ : Positive integers and the exponents of different prime factors, where i = 1, 2,….,n => number of prime factors = n We have to find the number of different factors of $$4^5+4^6+4^7$$ => $$4^5+4^6+4^7$$ = $$4^5+4^5\cdot4^1+4^5\cdot4^2$$ => $$4^5\left(1+4^1+4^2\right)$$ => $$4^5\left(1+4+16\right)$$ => $$4^5\cdot21$$ => $$\left(2^2\right)^5\cdot3\cdot7$$ => ∴ Prime factors 2, 3 and 7 => ∴ Number of prime factors =3 Therefore, B is the correct answer. Answer B Math Revolution The World's Most "Complete" GMAT Math Course! Score an excellent Q49-51 just like 70% of our students. [Free] Full on-demand course (7 days) - 100 hours of video lessons, 490 lesson topics, and 2,000 questions. [Course] Starting$79 for on-demand and $60 for tutoring per hour and$390 only for Live Online.
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