Question

Find the maximum power of 91 which exactly divides 78!?​

Answer 1

Answer:

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Step-by-step explanation:

The highest power of 91 is 6 that divides 78.

Answer 2

The maximum power of 91 which exactly divides 78! is $91^2.$

• 78! (78 factorial) is the product of all positive integers from 1 to 78, which is a very large number.
• To find the maximum power of 91 that exactly divides 78!, we can use the fact that for any prime number p and any non-negative integer n,$p^n$ exactly divides n! if and only if the greatest power of p that is less than or equal to n is $p^k$ where k is the largest non-negative integer such that $p^k$ divides n!
• For prime number 91, the greatest power of 91 that is less than or equal to 78 is $91^2.$ This can be verified by taking the square root of 78 which is 8.83, so the greatest power of 91 that is less than or equal to 78 is $91^2.$

So, The maximum power of 91 which exactly divides 78! is 91^2.

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