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33!=12^{x} * y

find maximum integral value of x

Note by G J
3 years, 11 months ago

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The maximum integral value of x is 15.

We consider the highest prime in order to make divisibility to the said number 33!.

Since 33! = 1. 2. 3. 4.... 31. 32. 33

The numbers divisible by 3 are 3, 6, 9, 12, 15,... 30, 33.

Taking the powers of 3 divisible by these numbers, the highest power of 3 that divides by 33! is 3^15.

Taking the powers of 2 from the even numbers, the highest power of 2 that divides 33! is 41.

Since 12^x = 2^(2x) . 3^x

The highest power of 12 that divides 33! is 15.

John Ashley Capellan - 3 years, 11 months ago

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