Posted by K - NEED HELP on Wednesday, March 13, 2013 at 8:20pm.
If you multiply 100!*200!*300!, how many 0s are there?
MATH- HELP - Reiny, Wednesday, March 13, 2013 at 8:52pm
Think of all the factors that will produce a zero
1. clearly all multiples of 10 will add a zero
that is, numbers like 30, 60, 210, etc
2. also every factor ending in 2 multiplied by a factor ending in 5 will produce a zero
so zeros are produced by the following
* 2 * * 5 * * * * 10 * 12 * * 15 * * * * 20 * ....
so for the first 10! we should have 2 zeros, test with your calculator to get 3628800
by the time we get to 20! we should have 4 zeros
at 30! we should have 6 zeros
so after 100! we should have 20 zeros
by the same reasoning:
200! should have 40 zeros
300! should have 60 zeros
so we have (a x 10^20)(b x 10^40)(c x 10^60)
= abc x 10^120
check my thinking.
MATH- HELP - K - NEED HELP, Wednesday, March 13, 2013 at 9:26pm
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