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Olympiad workbook
Exam
Olympiad workbook
Subject
IOQM
Chapter
Permutation and Combination

Olympiad workbook · IOQM · Permutation and Combination

Find the number of positive integers n such that the highest power...

Find the number of positive integers nn such that the highest power of 7 dividing n!n! is 8 .

Correct answer

07

Step-by-step solution

Power of 7 in n!=n!=\left[\frac{n}{7}\right]+\left[\frac{n}{7^2}\right]+\ldots \frac{n}{7} \geq 7LetLetn=49Powerof7inPower of 7 inn!=7+1=8 nmayequaltomay equal to49,50,51,52,53,5455numberofpossiblevaluesofnumber of possible values ofn=07
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