Select the correct answerWhen 40! is expressed in base 8 form, what is the last non–zero digit in the base 8 expansion?radio_button_unchecked2radio_button_unchecked6radio_button_unchecked4radio_button_unchecked2 or 6
Question
Select the correct answerWhen 40! is expressed in base 8 form, what is the last non–zero digit in the base 8 expansion?radio_button_unchecked2radio_button_unchecked6radio_button_unchecked4radio_button_unchecked2 or 6
Solution
The question is asking for the last non-zero digit when 40! (factorial of 40) is expressed in base 8.
To solve this, we need to understand that the last non-zero digit in a factorial in base 8 is determined by the product of the last non-zero digits of each of the numbers from 1 to 40 in base 8.
However, any number that ends in 0 in base 8 will contribute a 0 to the end of the factorial, and any number that is a multiple of 8 will end in 0 in base 8.
Therefore, we only need to consider the numbers from 1 to 7, repeated 5 times (since 40 divided by 8 is 5).
The last non-zero digits of the numbers from 1 to 7 in base 8 are: 1, 2, 3, 4, 5, 6, 7.
Multiplying these together, we get 5040.
Expressing 5040 in base 8, we get 11600.
Therefore, the last non-zero digit in the base 8 expansion of 40! is 6.
So, the correct answer is 6.
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