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If n = 9! – 6^4, which of the following is the greatest inte [#permalink]
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\(9!=6*(3*2)*(4*9)*8*7*5*1\); \(9!=6^4*280\)
\(6^4(280-1)\) is divisible by 3 in both \(6^4\) and \(279\) factors
\((2*3)^4(9*31)\) divided by \(3^k\) results in \(k=6\) and answer is D
Carcass wrote:
If \(n = 9! – 6^4\), which of the following is the greatest integer k such that \(3^k\) is a factor of n ?

A. 1
B. 3
C. 4
D. 6
E. 8
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Re: If n = 9! 6^4, which of the following is the greatest inte [#permalink]
one alternative to the solution is to calculate it using calculator. Since 9! - 6^4 = 362880 , now keep trying different ways by dividing 362880 / (3^(options from the choices) )

Since its asking to give us largest number, we can start from 8 which is largest option and go above. If its fully divisible, it won't give us point. Therefore this way this will give us the answer
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Re: If n = 9! 6^4, which of the following is the greatest inte [#permalink]
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jagupta wrote:
one alternative to the solution is to calculate it using calculator. Since 9! - 6^4 = 362880 , now keep trying different ways by dividing 362880 / (3^(options from the choices) )

Since its asking to give us largest number, we can start from 8 which is largest option and go above. If its fully divisible, it won't give us point. Therefore this way this will give us the answer



You wont be able to calculate this using a calculator on the actual exam coz its a large no, so the best approach would be to prime factorize it
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Re: If n = 9! 6^4, which of the following is the greatest inte [#permalink]
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