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Integer m has 4 different prime factors and n has 3 different prime
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22 Mar 2017, 12:07
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Integer m has 4 different prime factors and n has 3 different prime factors. If m and n has the greatest common factor of 15, how many different prime factors does mn have? (A) 4 (B) 5 (C) 6 (D) 7 (E) 8
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I guess that 3 and 5 are common to both m and n. Besides that m has 2 unique prime factors and n has 1 unique factor making a total of 5 prime factors IMO answer is B
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Re: Integer m has 4 different prime factors and n has 3 different prime
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22 Mar 2017, 12:27
Answer should be B as the there will be 3 prime numbers in addition, so in total we will have 5 different prime numbers,



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Re: Integer m has 4 different prime factors and n has 3 different prime
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22 Mar 2017, 12:36
I have a doubt my answer is coming out to be 4
Like I took m to be 210 which has 4 prime factors2,3,5,7 and n to be 30 which has 3 prime factors2,3,5
now mn is 6300 which has 4 prime factors2,3,5,7



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Integer m has 4 different prime factors and n has 3 different prime
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22 Mar 2017, 14:05
johncath wrote: I have a doubt my answer is coming out to be 4
Like I took m to be 210 which has 4 prime factors2,3,5,7 and n to be 30 which has 3 prime factors2,3,5
now mn is 6300 which has 4 prime factors2,3,5,7 Hello, I took the same approach as yours i.e. by listing 2 sets of integers which have only prime factors. The answer must be B. The error in the numbers you chose is as follows, 210 = 2x3x5x7 30 = 2x3x5 GCF of 210 and 30 is 2x3x5 = 30 and not 3 x 5 = 15. Thus the numbers you selected should have been: 210 = 2x3x5x7 and 165 = 3x5x11 such that GCF = 3 x 5 = 15. With this combination now, Number of prime factors of mn = Count(2, 3, 5, 7, 11) = 5. Correct AC is B Hope that helps.



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Re: Integer m has 4 different prime factors and n has 3 different prime
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22 Mar 2017, 20:12
ThePhDAspirant wrote: johncath wrote: I have a doubt my answer is coming out to be 4
Like I took m to be 210 which has 4 prime factors2,3,5,7 and n to be 30 which has 3 prime factors2,3,5
now mn is 6300 which has 4 prime factors2,3,5,7 Hello, I took the same approach as yours i.e. by listing 2 sets of integers which have only prime factors. The answer must be B. The error in the numbers you chose is as follows, 210 = 2x3x5x7 30 = 2x3x5 GCF of 210 and 30 is 2x3x5 = 30 and not 3 x 5 = 15. Thus the numbers you selected should have been: 210 = 2x3x5x7 and 165 = 3x5x11 such that GCF = 3 x 5 = 15. With this combination now, Number of prime factors of mn = Count(2, 3, 5, 7, 11) = 5. Correct AC is B Hope that helps. Ah Got it! Thanks alot mate:)



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Integer m has 4 different prime factors and n has 3 different prime
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22 Mar 2017, 23:01
Bunuel wrote: Integer m has 4 different prime factors and n has 3 different prime factors. If m and n has the greatest common factor of 15, how many different prime factors does mn have?
(A) 4 (B) 5 (C) 6 (D) 7 (E) 8 Since m has 4 different prime factors and n has 3 different prime factors let the prime factors of m be a,b,3 and 5let the prime factors of n be c,3 and 5Since the GCD(m,n)=15, both m and n will have 3 and 5 as common prime factors now m*n will have the following prime factors a,b,c,3 and 5 which are 5 in number. Hence option B is correct. Hit Kudos if you liked it



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Re: Integer m has 4 different prime factors and n has 3 different prime
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26 Mar 2017, 01:11
Integer m has 4 different prime factors and n has 3 different prime factors. If m and n has the greatest common factor of 15, how many different prime factors does mn have?
(A) 4 (B) 5 (C) 6 (D) 7 (E) 8
Now M has 4 prime factors and n has 3.
the GCF is the greatest comman factore since it is 15 we see the prime factors for 15 and they are 3*5
so 2 of the Ms prime factor are 3 and 5 and left 2 other prime factors, 2 of the Ns prime factor are 3 and 5 left 1 other prime factor
2+(2)+1=5



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Re: Integer m has 4 different prime factors and n has 3 different prime
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26 Mar 2017, 09:51
Bunuel wrote: Integer m has 4 different prime factors and n has 3 different prime factors. If m and n has the greatest common factor of 15, how many different prime factors does mn have?
(A) 4 (B) 5 (C) 6 (D) 7 (E) 8 The Answer should be B. m = A*B*C*D n = X*Y*Z Both have powers >= 1. GCD (M,N) = 3*5 => 3 and 5 are common prime factors. => 2 + 3 additional factors so a total of 5 factors. Correct?
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Re: Integer m has 4 different prime factors and n has 3 different prime
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26 Mar 2017, 11:13
M has 4 different prime factors M  2 x 3 x 5 x 7 = 210
N has 3 different prime factors N  3 x 5 x 11 = 165
MN = 210 x 165 = 34650
34650 has 5 different prime factors (2, 3, 5, 7 and 11).
The answer is B



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Re: Integer m has 4 different prime factors and n has 3 different prime
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27 Mar 2017, 11:55
Bunuel wrote: Integer m has 4 different prime factors and n has 3 different prime factors. If m and n has the greatest common factor of 15, how many different prime factors does mn have?
(A) 4 (B) 5 (C) 6 (D) 7 (E) 8 If m and n have a GCF of 15, they both share a prime of 3 and 5. Thus, m has 2 prime factors that differ from those of n and n has 1 other prime factor that differs from those of m. Since mn has 2 common prime factors and 3 uncommon prime factors, mn has a total of 5 different prime factors. Answer: B
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Re: Integer m has 4 different prime factors and n has 3 different prime
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19 Mar 2019, 07:10
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