Question

find maximum power of 6 in 75!​

Answer 1

$\huge \underline \bold \green{QUESTION}:$

$find \: the \: maximum \: power \: of \: 6 \: in \: 75 \: !$

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$\huge \underline \bold \red{SOLUTION}:$

we should use the following formula and

in the solution [.] represents greatest integer funtion

$[ \frac{n}{ {p}^{1} } ] + [ \frac{n}{ {p}^{2} } ] + [ \frac{n}{ {p}^{3} } ] + ..... \\ = > here \: n = 75 \: and \: p = 6 \\ = > [ \frac{75}{ {6}^{1} } ] + [ \frac{75}{ {6}^{2} } ] + [ \frac{75}{ {6}^{3} } ] + ..... \\ = > [ \frac{75}6 ] + [ \frac{75}{ 36 } ] + [ \frac{75}{ 216 } ] + ..... \\ = > 12 + 2 + 0 + 0 + ..... \\ = > 14$

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$\underline\bold \red{final \: answer} :$

$\boxed{ \green{powers \: = 14}}$

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$\underline\bold \red{formulas \: used} :$

$[ \frac{n}{ {p}^{1} } ] + [ \frac{n}{ {p}^{2} } ] + [ \frac{n}{ {p}^{3} } ] + .....$

hope it helps you