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Director
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Re: What portion of the set of unique factors of the product of 24 and 385
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11 Jul 2019, 18:11
What portion of the set of unique factors of the product of 24 and 385 are prime factors?
24*385= 2^3*3*5*7*11 Total number of unique factors= 4*2*2*2*2=64 Prime factors= 5
Probability= 5/64
IMO C



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Re: What portion of the set of unique factors of the product of 24 and 385
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11 Jul 2019, 18:37
The number of unique factors for 24*85 are
24*85=2^3*3*5*7*11 So (3+1)*(1+1)*(1+1)*(1+1)*(1+1) =64
And out of then prime are 2,3,5,7,11
Therefore 5/64
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Re: What portion of the set of unique factors of the product of 24 and 385
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11 Jul 2019, 19:06
What portion of the set of unique factors of the product of 24 and 385 are prime factors?
If we decompose 24*385 into prime factors we get: 2^3 * 3 * 5 *7 *11.
so we have 5 prime factors and # of factors is (3+1)*(2)*(2)*(2)*(2)= 2^6 = 64
so the result is 5/64, (C) is our answer.



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Re: What portion of the set of unique factors of the product of 24 and 385
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11 Jul 2019, 19:17
\(24*385 = 2^33^15^17^111^1\), so number of unique factors \(= 4*2*2*2*2 = 64\) and the prime factors involved are \(2,3,5,7,11\) ,i.e \(5\) primes so the portion = \(\frac{5}{64}\)
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Re: What portion of the set of unique factors of the product of 24 and 385
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11 Jul 2019, 20:12
factors of the product
1  2  3  4  5  6  7  8  10  11  12  14  15  20  21  22  24  28  30  33  35  40  42  44  55  56  60  66  70  77  84  88  105  110  120  132  140  154  165  168  210  220  231  264  280  308  330  385  420  440  462  616  660  770  840  924  1155  1320  1540  1848  2310  3080  4620  9240
5 distinct prime numbers
so 5/64



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Re: What portion of the set of unique factors of the product of 24 and 385
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11 Jul 2019, 20:37
24=\(2^3\)*3. Overall factors are 4*2=8 385=5*7*11. Overall factors are 2*2*2=8 So product of 24*385 has 64 factors (8*8) Unique factors are 2,3,5,7,11 (5 in total)  5/64 (C)



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Re: What portion of the set of unique factors of the product of 24 and 385
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11 Jul 2019, 21:09
24 and 385 for the product is 24 and 385 = 8*3* 5*7*11 =\(2^3∗3∗5∗7∗11\) hence total number of prime factors =\((3+1)∗2∗2∗2∗2\)= 64 but total number of prime factors will be 2,3,5,7,11 = 5 hence fraction =\(\frac{5}{64}\) Answer C



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Re: What portion of the set of unique factors of the product of 24 and 385
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11 Jul 2019, 21:34
Number of factors of product of 24 and 385(2^3*3^1*7*11*5) = 8*8=64 Prime factors = 2,3,5,7,11 Hence 5/64 Answer is C
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Re: What portion of the set of unique factors of the product of 24 and 385
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11 Jul 2019, 21:43
Product of 24 and 385 = 9240 \(9420 = 2^3 * 3 * 5 * 7 * 11\)
Number of Prime factors = 5 Number of unique Positive Factors = (3 + 1) * (1 + 1) * (1 + 1) * (1 + 1) * (1 + 1) = 64
Therefore, the portion we are looking for is \(\frac{5}{64}\)
Answer C



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Re: What portion of the set of unique factors of the product of 24 and 385
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11 Jul 2019, 21:47
What portion of the set of unique factors of the product of 24 and 385 are prime factors?
here, 24= 2^3 * 3 385= 5*7*11 there are 5 prime factor total factor = (3+1)*(1+1)*(1+1)*(1+1)*(1+1) =64
So, the correct answer choice is (C)



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Re: What portion of the set of unique factors of the product of 24 and 385
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11 Jul 2019, 22:01
Question is asking for the fraction of the unique set of factors of 24 * 385. That is, # of unique factors divided by total # of factors.
First, find the prime factorization of the product of 24 and 385.
24 * 385 = 2^3*3*5*7*11
Total # of factors of any number with prime factorization, x^a*y^b*z^c = (a+1)(b+1)(c+1)
From above Total # of factors of the product 24 * 385 = 4*2*2*2*2 = 64
There are 5 unique factors of this product. They are 2, 3, 5, 7, 11.
Hence the portion of the set of unique factors of 24 * 385 = 5/64
Correct answer C



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Re: What portion of the set of unique factors of the product of 24 and 385
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11 Jul 2019, 22:28
rephrase the question x portion of Y factors of 24*285 are prime factors.. x = no of prime factors in the product / total unique factors in 24*385
24 = 2^3 * 3^1 = 8 total factors  unique prime factors are 2, 3 385 = 5^1 * 7^1 * 11^1 = 8 total factors  unique prime factors 5, 3, 7
combined there are 5 unique prime factors total factors  8 * 8 portion is 5/64
C , is the answer!



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Re: What portion of the set of unique factors of the product of 24 and 385
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11 Jul 2019, 22:57
product of 24 and 385 = 24x385 > (2^3x3) x (5x7x11) > total unique factors are = (3+1)(1+1)(1+1)(1+1)(1+1) = 64, prime factors = 2,3,5,7, and 11, so the answer is 5/64 (C)



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Re: What portion of the set of unique factors of the product of 24 and 385
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11 Jul 2019, 23:30
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Re: What portion of the set of unique factors of the product of 24 and 385
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11 Jul 2019, 23:47
24 = 2^3 * 3
385 = 5 * 7 * 11
24 * 385 = 2^3 * 3 * 5 * 7 * 11
Total no. of factors of 24 * 385 = (3+1) * (1+1) * (1+1) * (1+1) * (1+1) = 64
Prime factors of the product are 2, 3, 5, 7, and 11 ie, no of prime factors = 05
Hence, proportion needed = 5/64
Answer: C



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What portion of the set of unique factors of the product of 24 and 385
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Updated on: 12 Jul 2019, 08:25
What portion of the set of unique factors of the product of 24 and 385 are prime factors?
Product can be rewritten as = 24*385 = 6*4 *77*5 = 2*3*2*2*11*7*5 =\(2^3 *3^1*5^1* 7^1* 11^1\) So total number of unique factor = (3+1)*(1+1)*(1+1)*(1+1)*(1+1) = 4*2*2*2*=4*16 = 64
prime factors are = 2,3,5,7,11 = 5
So 5 of 64 are prime factors = 5/64 = Option C
Originally posted by baru on 11 Jul 2019, 23:56.
Last edited by baru on 12 Jul 2019, 08:25, edited 1 time in total.



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What portion of the set of unique factors of the product of 24 and 385
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Updated on: 12 Jul 2019, 10:01
Soln:
prime factors of 24 :2,2,2,3 Prime factors of 385: 5,7,11
Product of 24 and 385 will have total prime factors:(3+1) (1+1) (1+1)(1+1)(1+1) TOTAL COUNT 64 unique prime factors : 2,3,5,7,11 ( Total count 5)
So portion of the set of unique factors of the product of 24 and 385 are prime factors 5/64
CORRECT ANS C
Originally posted by komals06 on 12 Jul 2019, 00:08.
Last edited by komals06 on 12 Jul 2019, 10:01, edited 1 time in total.



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Re: What portion of the set of unique factors of the product of 24 and 385
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12 Jul 2019, 01:14
IMOC
24 X 385 = 2^3 * 3 * 5 * 7 * 11 No of factors= 4*2*2*2*2= 64 Prime Factors= 5
Req Fraction= 5/64
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Re: What portion of the set of unique factors of the product of 24 and 385
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12 Jul 2019, 01:22
What portion of the set of unique factors of the product of 24 and 385 are prime factors?
(A) 5 7
57
(B) 7 32
732
(C) 5 64
564
(D) 6 64
664
(E) 7 64
764
Solutions: Factors of 24=\(2^3\) *3 Factors of 385=5 * 7* 11 Unique Factors=2 * 3 *5 * 7 * 11 Number of unique factors =5 Total number of prime factors =(3+1)(1+1)((1+1)(1+1)(1+1)=4*2*2*2*2=64 The portion of set of unique factors of the product of 24 and 385=\(\frac{5}{64}\)



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Re: What portion of the set of unique factors of the product of 24 and 385
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12 Jul 2019, 02:15
prime factorization of \(24*385= 2^3*3*5*7*11\) Total number of factors \(= (3+1)*(1+1)*(1+1)*(1+1)*(1+1)= 64\) Distinct prime factors \(= (2,3,5,7,11)= 5\) Required ratio \(=\frac{5}{64} .\) IMO C
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Re: What portion of the set of unique factors of the product of 24 and 385
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