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The total # of prime factors of the product

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Senior Manager
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The total # of prime factors of the product [#permalink] New post 09 Jan 2004, 14:33
The total # of prime factors of the product (8)^23*(21)^19*(13)^15 is?

a.118
b.119
c.4
d.57

***Any ideas on how to crack this one?
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 [#permalink] New post 09 Jan 2004, 16:27
but I got 122 as the total number of prime factors

8^23 can be written as (2^3)*23= 2^69, so 69 as prime factor

21^19 can be written as(3*7)^19=3^19 and 7^19, so 19+19

13^15 = 15 so total number =69+19+19+15=122
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 [#permalink] New post 09 Jan 2004, 16:41
I got the same as Rakesh did... 122

I guess it would be 4 if the question asked for the number of "different" prime factors.


But 122 is not among the choices... so... what should we do?
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 [#permalink] New post 09 Jan 2004, 16:56
The official answer is 119
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 [#permalink] New post 09 Jan 2004, 17:08
oh god 119 then is there any way to do it
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 [#permalink] New post 09 Jan 2004, 19:49
sunniboy007 wrote:
The official answer is 119


i stand stupid :roll:
i considered different prime factors :?: i was thinking too much :shock:
  [#permalink] 09 Jan 2004, 19:49
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