Problem Solving (PS) | ­What is the highest power of 3 available in the expression 58! - 38!?

­58! - 38! =

= 38!(58 * 57 * 56 * ... * 39 - 1)

58 * 57 * 56 * ... * 39 is a multiple of 3, thus 58 * 57 * 56 * ... * 39 - 1 is 1 less than a multiple of 3, so not a multiple of 3 and thus will not contribute any 3's to the entire product.

The highest integer power of 3 in 38! is 38/3 + 38/9 + 38/27 = 12 + 4 + 1 = 17 (remember we take only the quotients of the divisions, that is 38/3 would give 12, not 12 2/3).

Answer:A­.

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For theory on the topic discussed in the question check: NumberProperties

For similar questions check the following topics from our Special QuestionsDirectory :

12. TrailingZeros
13. Power of a number in afactorial

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