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by vinviper1 » Mon Apr 14, 2008 12:50 pm
The product of all the prime numbers less than 20 is closet to which of the folowing powers of 10?

10^9
10^8
10^7
10^6
10^5

[spoiler]10^7[/spoiler]
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by dalwow » Tue Apr 15, 2008 7:48 am
Is the answer 10^6?

I just ran it through my head roughly...we can see that 2*3*5*7 = 210.
All the prime numbers after that will add a 0 to the end of the 210 because each is greater than 10, but less than 20. So, we have 11, 13, 17, 19...we add 4 zeros which gives us 2100000. That would be closest to 10^6 I believe.
I know there are others here much better at this than I, so I hope someone will correct me if I'm wrong.
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by simplyjat » Tue Apr 15, 2008 8:10 am
The answer is 10^7...
Actually there is no shortcut to this type of question, only way is to do the actual multiplication, taking two at a time...

2*3*5*7 = 210 as discussed earlier
210 * 11 = 2310
2310 * 13 = 30030
30030 * 17 = 510510
510510 * 19 = 9699690 ~ 10^7
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by dalwow » Tue Apr 15, 2008 8:16 am
Thanks simplyjat, I see I was very wrong in my thinking.
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by vinviper1 » Tue Apr 15, 2008 1:03 pm
thanks.
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