Advanced Math/a problem

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Expert: Sherman D. - 1/21/2005


Question
Hi, I'd appreciate your help on this...thanks!

Question:
What is the greatest positive integer n such that 2^n is a factor of 12^10?

Answer
(6 * 2)^10 = ((2*2) * 3)^10
((2^2) * 3)^10
Same as saying
(2^2^10) * 3^10
same as saying
2^(2 * 10) * 3^10
becomes
2^20 * 3^10
ANS : n = 20

And that is how you get the answer.

Proof/Checked

12^10
61917364224
2*30958682112
2*2*15479341056
2*2*2*7739670528
2*2*2*2*3869835264
2*2*2*2*2*1934917632
2*2*2*2*2*2*967458816
2*2*2*2*2*2*2*483729408
2*2*2*2*2*2*2*2*241864704
2*2*2*2*2*2*2*2*2*120932352
2*2*2*2*2*2*2*2*2*2*60466176
2*2*2*2*2*2*2*2*2*2*2*30233088
2*2*2*2*2*2*2*2*2*2*2*2*15116544
2*2*2*2*2*2*2*2*2*2*2*2*2*7558272
2*2*2*2*2*2*2*2*2*2*2*2*2*2*3779136
2*2*2*2*2*2*2*2*2*2*2*2*2*2*2*1889568
2*2*2*2*2*2*2*2*2*2*2*2*2*2*2*2*944784
2*2*2*2*2*2*2*2*2*2*2*2*2*2*2*2*2*472392
2*2*2*2*2*2*2*2*2*2*2*2*2*2*2*2*2*2*236196
2*2*2*2*2*2*2*2*2*2*2*2*2*2*2*2*2*2*2*118098
2*2*2*2*2*2*2*2*2*2*2*2*2*2*2*2*2*2*2*2*59049
2*2*2*2*2*2*2*2*2*2*2*2*2*2*2*2*2*2*2*2*3*19683
2*2*2*2*2*2*2*2*2*2*2*2*2*2*2*2*2*2*2*2*3*3*6561
2*2*2*2*2*2*2*2*2*2*2*2*2*2*2*2*2*2*2*2*3*3*3*2187
2*2*2*2*2*2*2*2*2*2*2*2*2*2*2*2*2*2*2*2*3*3*3*3*729
2*2*2*2*2*2*2*2*2*2*2*2*2*2*2*2*2*2*2*2*3*3*3*3*3*243
2*2*2*2*2*2*2*2*2*2*2*2*2*2*2*2*2*2*2*2*3*3*3*3*3*3*81
2*2*2*2*2*2*2*2*2*2*2*2*2*2*2*2*2*2*2*2*3*3*3*3*3*3*3*27
2*2*2*2*2*2*2*2*2*2*2*2*2*2*2*2*2*2*2*2*3*3*3*3*3*3*3*3*9
2*2*2*2*2*2*2*2*2*2*2*2*2*2*2*2*2*2*2*2*3*3*3*3*3*3*3*3*3*3

In Short 2^20 * 3^10

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Sherman D.

Expertise

I can answer questions dealing in mathematics of all kinds except for Physics and Calculus, but i can answer questions in Pre-Calculus and Chemistry. I can also answer questions in Recipes of all kinds. I can find games cheats/walkthroughs, but i can`t find a specific game online or offline. I can also do history and recipes for alcoholic beverages.

Experience

Mathematics, Recipes, History, and Games.

Education/Credentials
High School graduated. I graduated with honors, and i was in Beta Club for a year and a half.

Awards and Honors
Principle's list and A and B honor roll in high school only.

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