Product of prime numbers

**kannn** · 03-16-2007, 02:27 AM

Hi,

This is a simple question from Diagnostic section of OG11.Still I took so much time to slove it.If I work out at this rate then I guess I would be the least scorer ever

. Pls guys let me know if there is a shortcut for these kind of questions.

Q:The product of all the prime numbers less than 20 is closest to which of the following powers of 10?
A) 10^9
B) 10^8
C) 10^7
D) 10^6
E) 10^5

Do I've to multiply 2,3,5,7,11,13,17 and 19 to compare the answer? Is there a better way to do it?

Thanks

**EEMan** · 03-16-2007, 04:10 AM

2.3.5.7.11.13.17.19 = (2.5) . (3.7) . (10.1,1) . (10.1,3) . (10.1,7) . (10.1,9)
= 10^5 . (10.2,1).1,1.1,3.1,7.1,9 = 10^6 . (1,1.1,3.1,7.1,9.2,1) closest to 10^7

That's what I thought. I have not a better than this one.

**kannn** · 03-16-2007, 10:22 AM

EEMan,

Can u pls explain thy calc?

Thanks

**thankont** · 03-16-2007, 04:12 PM

like EEMan approach just giving another solution
2*5 = 10
19 close to 20= 2*10
3*7=21 close to 20 = 2*10
11 close to 10
13*17 = 221 close to 2*10^2 so
about (rough approx) 8*10^6 close to 10^7

**EEMan** · 03-16-2007, 08:46 PM

yeah it looks more simple. Thank you

**kevinspain** · 03-16-2007, 09:33 PM

Originally Posted by kannn

Hi,

This is a simple question from Diagnostic section of OG11.Still I took so much time to slove it.If I work out at this rate then I guess I would be the least scorer ever

. Pls guys let me know if there is a shortcut for these kind of questions.

Q:The product of all the prime numbers less than 20 is closest to which of the following powers of 10?
A) 10^9
B) 10^8
C) 10^7
D) 10^6
E) 10^5

Do I've to multiply 2,3,5,7,11,13,17 and 19 to compare the answer? Is there a better way to do it?

Thanks

Remember that you can multiiply numbers in whichever order you like!

2*3*5*7*11*13*17*19= (19*5)*(2*3*17)*(7*13*11) approx 100*100*1000

**purplepeopleeater** · 03-17-2007, 03:38 AM

it is a numbers property question. the "lazy genius" way is take the product of 2.5 and you get the base (10). Then, add 3,7,11,19, 13,17 = 70 or 10 to the 7th power

**purplepeopleeater** · 03-17-2007, 03:39 AM

its trying to drive you to the easy way to solve the question- base 10

**suithink** · 03-22-2007, 03:09 PM

The numbers are
2,3,5,7,11,13,17,19

Pair 2*19= 38 = 3.8 * 10
17*3= 5.1 *10
13*5=6.5 * 10
11*7= 7.7 * 10

So Powers of 10 = 4 + (4*5*7*8)=4+(2*10,5.6*10)..here I approx 3.8==> 4
=6+( 1)= 7....