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product of prime #'s

Expert replies
by rahul.s » Thu Jan 28, 2010 5:30 am
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

[spoiler]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[/spoiler]

Does anyone have a practical and usable method? Thanks in advance.
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Source: — Problem Solving |

by ajith » Thu Jan 28, 2010 5:47 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


5*19 = 95 close to 10^2

17*2*3 = 102 close to 10^2

7*11*13 = 1001 close to 10^3

Hence 10^( 2+2+3) = 10^7
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