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Finding out if 2003^2004  2005 is divisible by 10?by Virtate
Tags: divisibilty 
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#1
Oct705, 09:40 AM

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Hello,
I was wondering, how does one go finding out if 2003^2004  2005 is divisible by 10??? Or that 3^102 * 7^29 is divisible by 33??? If someone could help me, I would really appreciate it. Thank You. 


#2
Oct705, 09:55 AM

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We do help people with homework here, but you have to show how you started and where you got stuck.



#3
Oct705, 10:00 AM

P: 6

I only got as far as 2003 = 3 (mod 10), and I have no idea where to go from there. I think I'm headed in the wrong direction... If someone could give me a few pointers, that would be great.



#4
Oct705, 10:07 AM

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Finding out if 2003^2004  2005 is divisible by 10?
OK, in order for 2003^20042005 to be divisible by 10, it has to end in zero. That means that 2003^2004 has to end with 5 (because when you subtract 2005, you'll get a zero in the ones place). Now you should be able to tell pretty straighforwardly if 2003^2004 ends with 5.
As for the other one, any number that is divisible by 33 must be divisible by both 3 and 11. Since you were given the prime factorization of the other number, you should be able to tell just by looking whether it is divisible by 33. 


#5
Oct705, 10:11 AM

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Incidentally, it was me who moved your thread to the K12 HW section. I can see from your second thread that this is probably a College course, so I've moved both this thread and your other one to College HW.
Any and all homework questions go to this area, not in the Math section. 


#6
Oct705, 10:50 AM

P: 6

Thanks Tom!



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