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In how many ways can you express 160000 as a product of 2

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Director
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In how many ways can you express 160000 as a product of 2 [#permalink] New post 15 Sep 2006, 02:45
In how many ways can you express 160000 as a product of 2 different factors?

A 39
B 40
C 41
D 44
E 49
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Re: Factors of a number [#permalink] New post 15 Sep 2006, 02:54
Futuristic wrote:
In how many ways can you express 160000 as a product of 2 different factors?

A 39
B 40
C 41
D 44
E 49


This is how I started it, but couldn't get an answer:

160,000 can be expressed as (2^4)(10^4) = 20^4
20 has 6 factors (1,2,4,5,10,20)
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 [#permalink] New post 15 Sep 2006, 05:36
160000 = 10^4 x 2^4
= 5^4 x 2^4 x 2^4
= 2^8 x 5^4

# of factors of 16000 = (1+8)x(1+5) = 45

As we need atleast two different factors exclude 160000

Answer: D. 44
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 [#permalink] New post 15 Sep 2006, 06:02
haas_mba07 wrote:
160000 = 10^4 x 2^4
= 5^4 x 2^4 x 2^4
= 2^8 x 5^4

# of factors of 16000 = (1+8)x(1+5) = 45

As we need atleast two different factors exclude 160000

Answer: D. 44

Haas please explain this part
# of factors of 16000 = (1+8)x(1+5) = 45 I don't understand it.Thanks in advance
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 [#permalink] New post 15 Sep 2006, 06:09
When you convert the number into its prime factors

16000 = 2^8 x 5^4

Now as per a rule to find number of factors is in the following thread:

http://www.gmatclub.com/phpbb/viewtopic ... ht=#241853


In general to find the number of divisors you find the total number of factors of each term (don't forget 1) ....

In this case for 2^8 the factors are : 1, 2, 4, 8, ... 2^8
which is 9 (1+8)

For 5, the total number of factors are : 1,5, ... 5^4 which is a total of 5 (1+4)

Therefore total factors = 9 x 5 = 45.

Note that in the thread I linked you can extend the same notion to find the sum of all factors...

Yurik79 wrote:
Haas please explain this part
# of factors of 16000 = (1+8)x(1+5) = 45 I don't understand it.Thanks in advance
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 [#permalink] New post 15 Sep 2006, 06:17
Haas on target again. OA is D
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 [#permalink] New post 15 Sep 2006, 10:59
haas_mba07 wrote:
When you convert the number into its prime factors

16000 = 2^8 x 5^4

Now as per a rule to find number of factors is in the following thread:

http://www.gmatclub.com/phpbb/viewtopic ... ht=#241853


In general to find the number of divisors you find the total number of factors of each term (don't forget 1) ....

In this case for 2^8 the factors are : 1, 2, 4, 8, ... 2^8
which is 9 (1+8)

For 5, the total number of factors are : 1,5, ... 5^4 which is a total of 5 (1+4)

Therefore total factors = 9 x 5 = 45.

Note that in the thread I linked you can extend the same notion to find the sum of all factors...

Yurik79 wrote:
Haas please explain this part
# of factors of 16000 = (1+8)x(1+5) = 45 I don't understand it.Thanks in advance

Thanks a tone Haas
I think we have a new math guru here :king
Your solutions are awesome man
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  [#permalink] 15 Sep 2006, 10:59
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