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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, 09:16
Quote: What portion of the set of unique factors of the product of 24 and 385 are prime factors?
(A) 5/7 (B) 7/32 (C) 5/64 (D) 6/64 (E) 7/64 Rule: num.factor(x) is equal to the product of the "power+1" of its prime factors prime factors of (24)=(2ˆ3•3) prime factors of (385)=(7•11•5) num.factors(24•385)=(2ˆ3•3•7•11•5)=(3+1)(1+1)(1+1)(1+1)(1+1)=64 no. of primes / total num factors = 5 {2,3,7,11,5} /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, 09:26
Prime factorisation of \(24*385 = 2^3 * 3 *5*7*11\)
Total number of factors = \(4*2*2*2*2 = 64\)
Number of prime factors = 5
So fraction of prime factors = 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, 09:32
To solve for the unique prime factors of the product of 24 and 385. The factors are as follows: 24 = 1,2,3,4,6,8,12,24 385 = 1,5,7,11,35,55,77,385 multiplying the 24 and 385 will generate the following factors; 1,2,3,4,5,6,7,8,9,10,11, and so on. Thus the unique prime factors of the product of 24 and 385 are 2,3,5,7, and 11. Only answer choice with 5 as numerator is "A" and "C". Since the unique factors of the product is more than 7 Hence answer choice "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: 11 Jul 2019, 10:12
The answer is 5/64 here is why
24 = 2^3 * 3. (2 unique primes)
385 = 5 * 7 * 11 (3 unique primes)
Total number of factors: 4 * 2 * 2 * 2 * 2 ( take exponents of prime factorization add one to each them multiply to get total number of factors). This yields 8 *8 = 64
You get 5/64
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Originally posted by Peter2719 on 11 Jul 2019, 09:51.
Last edited by Peter2719 on 11 Jul 2019, 10:12, 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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11 Jul 2019, 09:53
What portion of the set of unique factors of the product of 24 and 385 are prime factors? breakdown the product into prime factors; 2^3 * 3 * 5 * 7 * 11; (2,3,5,7,11 > 5 unique factors) in total there are (3+1)(2)(2)(2)(2)= 64 unique factors ; ans: c 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, 09:55
Working on the stem: \(24*385=2^3*3*5*7*11\)
We need to find: number of prime factors/total number of positive factors
number of prime factors: 5 Total number of factors: 4*2*2*2*2=64
IMO Ans: 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, 09:55
What portion of the set of unique factors of the product of 24 and 385 are prime factors?
We need to find:
Numerator = UNIQUE PRIME FACTORS of (24x385)
Denominator = UNIQUE FACTORS of (24x385)
Start by finding prime factors of 24 and 385
24 = 2x2x2x3
385 = 5x7x11
So Prime factors of (24x385) = (2^3)*3*5*7*11
Unique prime foctors = 2,3,5,7,11..... NUMERATOR = 5
To get unique factors of a number, we need to add 1 to the power of each prime factors and multiply the resulting numbers. 2 has power 3 and others have power 1:
so, number of unique factors = (3+1)*2*2*2*2 = 64 = DENOMINATOR
ANSWER = C  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, 10:00
Prime factorisation of 24 is 2^3 X3, so distinct factors are 8 Prime factorisation of 385 is 5x7x11, so distinct factors are 8
Number of unique factors of product of 24 and 385 are 8x8 = 64. Out of them prime factors are 2,3,5,7,11. Total number of prime factors is 5
5 out of 64 factors are prime factors.
C is correct.



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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, 10:22
12*385 can be written as
2^3*3*11*7*5
No.of factors are 4*2*2*2*2=64
Now prime factors are 2,3,11,7,5
So answer is 5/64 that 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, 10:26
What portion of the set of unique factors of the product of 24 and 385 are prime factors?
24 can be written as 2X2X2X3 = 2 unique factor 385 can be written as 11X7X5 = 3 unique factor
24X385 = 5 unique prime factor and 64 total factor
5/64 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, 10:44
IMO C solving we get 2^3 *3*5*7*11, so total of 5 prime factors, with no of factors 3+1 *2*2*2*2= 64, 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, 11:15
What portion of the set of unique factors of the product of 24 and 385 are prime factors?
(A) \(\frac{5}{7}\)
(B) \(\frac{7}{32}\)
(C) \(\frac{5}{64}\)
(D) \(\frac{6}{64}\)
(E) \(\frac{7}{64}\)
Product of 24 and 385= 24*385=\(2^3\) * 3 * 5 * 7 * 11
So the number of unique factors= (3+1) * (1+1) *(1+1) * (1+1)= 64
Number of prime factors= 5 > portion of the set of unique factors of the product of 24 and 385 are prime factors = \(5/64\)
IMO. the correct 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, 11:39
24*385=\(2^{3}\)*3*5*7*11 Total Number of factors of 24*385=4*2*2*2*2=64 Number of unique prime factors=5 {2,3,5,7,11} Required ratio=\(\frac{5}{64}\) Ans: 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, 12:19
total factors of 24 and 385 = 64 Different prime factors of 24 and 385 is 2,3,5,7,11 portion = 5/64 Hence ans 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, 12:29
What portion of the set of unique factors of the product of 24 and 385 are prime factors?
Our answer would be : \(\frac{unique factors 24*385}{total factors of 24*385}\)
24 = 3 * \(2^3\) 385 = 5*7*11
So, unique factors are : 2, 3, 5, 7, 11 => Total number = 5 Total number of factors [2*4] * [2*2*2] = 64 (Power of each prime factor+1 & multiplication)
So, our answer should be (C)\(\frac{5}{64}\)



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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, 13:19
What portion of the set of unique factors of the product of 24 and 385 are prime factors? total primes numbers are 5 and the total set of numbers would be 24 = 2^3*3 factors of 24= (3+1)*(1+1)= 8 385 = 5*11*7 factors of 385 = (1+1)*(1+1)*(1+1)= 8 Product of 24 * 385 so factors will be 8*8 = 64 prime numbers / factors = 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, 13:31
Prime factorization of 24*385 is (2^3)*3*5*7*11 But the number of unique factors of a number which has a prime factorization of (a^x)*(b^y) where a and b are prime numbers and x and y are integers equals (x+1)*(y+1). Hence the unique factors of 24*385=(4)(2)(2)(2)(2)=64. There are 5 prime factors, Hence portion of unique factors which are prime =5/64.
Answer therefore 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, 13:38
Total factors of: 24 2*2*2*3 385 5*7*11
Therefore:fav outcome/ Total outcome ==>5/7 IMOA
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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, 13:43
only 2,3, 5, 7 & 11 are prime factors of 9240 out of 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, 16:52
24=2^3 *3 385=5*7*11
Total no of factors in it's products =(3+1)(1+1)(1+1)(1+1)(1+1)= 64 Total prime factors=5
Ratio =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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