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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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