5. Find the largest power of 7 that...
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5. Find the largest power of 7 that can exactly divide 777! (A) 120 (B) 128 (C) 111 (D) 125

JEE/Engineering Exams
Maths
Solution
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Highest poules of 8 cactorial is ginen by ( left[frac{x}{n}right]+left[frac{x}{n^{2}}right]+left[frac{x}{n^{3}}right] ) where ( [cdot] ) refresents greatest integer the series gees on until greatest integer becomes 0 So, highest peren of 7 in 7771 ( =left[frac{77}{8}right]+left[frac{777}{49}right]+left[frac{777}{343}right] ) ( +left[frac{777}{2401}right] ) ( =111+15+2+0 ) ( =128 ) is requiered answer.
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