product of prime #'s

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rahul.s
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Topic: product of prime #'s

Thu Jan 28, 2010 6:30 am

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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

OA: C
Source: OG

OG's explanation: The prime numbers less than 20 are 2, 3, 5, 7, 11, 13, 17, and 19. Th eir product is 9,699,690 (arrived at as follows: 2*3*5*7*11*13*17*19 = 9,699,690). This is closest to 10,000,000 = 10^7

Does anyone have a practical and usable method? Thanks in advance.

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ajith
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Thu Jan 28, 2010 6:47 am

rahul.s wrote: 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 2, 3, 5, 7, 11, 13, 17, and 19 519 = 95 close to 10^2 1723 = 102 close to 10^2 711*13 = 1001 close to 10^3 Hence 10^( 2+2+3) = 10^7 _________________ Always borrow money from a pessimist, he doesn't expect to be paid back.