Question

if 54! power20 is completely divisible by 2power a^3 so the maximum value of a
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Answer 1

Step-by-step explanation:

Since 24 = 2^3 x 3, we see that there are fewer factors of 2^3 than factors of 3 in 50!, so we need to determine the number of factors of 2 in 50!. To do that, we can divide 50 by 2 successively as long as the quotient is nonzero and ignore the remainder whenever it’s nonzero.

50/2 = 25

25/2 = 12

12/2 = 6

6/2 = 3

3/2 = 1

Now, the number of factors of 2 in 50! is 25 + 12 + 6 + 3 + 1 = 47. Since 47/3 = 15 ⅔, there are 15 factors of 2^3 in 50!, and hence n = 15.