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05 Jun 2018, 22:41
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B
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
75%
(hard)
Question Stats:
57% (02:19) correct
43%
(02:38)
wrong
based on 438
sessions
History
Date
Time
Result
Not Attempted Yet
How many factors of 9600 are not divisible by 12?
A) 48
B) 30
C) 24
D) 20
E) 42
A) 48
B) 30
C) 24
D) 20
E) 42
CAMANISHPARMAR
Let's write 9600 in prime factorization form, 9600=\(2^7\)*\(5^2\)*\(3^1\)
Hence the no of factors of 9600=(7+1)(2+1)(1+1)=8*3*2=48
The no factors of 9600 not divisible by 12=Total of no factors of 9600- Total no of factors of 9600 which are divisible by 12
Now we can write, 9600=\(2^7\)*\(5^2\)*\(3^1\)=\(2^2\)*3(\(2^5\)*\(5^2\))=12(\(2^5\)*\(5^2\))
Since 12(\(2^5\)*\(5^2\)) is multiple of 12, hence the no of factors which are divisible by 12 =(5+1)(2+1)=6*3=18
Therefore,the no factors of 9600 not divisible by 12=48-18=30
Answer option(B)
General Discussion
07 Jun 2018, 04:32
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9600 could be written as 12 * 800
Now 10 is a factor of 800, so is 20, so is 400, including many others.
10, 20 and 400 are not divisible by 12 but (12*10), (12*20) and (12*400) are divisible by 12 because we are multiplying and dividing my 12. Hence every factor of 800 is also a factor of 9600 and is divisible by 12 if we are multiplying each factor of 800 by 12.
To find the number of factors of 800 is a straightforward application of number of factors formula:-
(p+1)(q+1)(r+1)... [where p,q,r are exponents of each prime factor]
Therefore 800 can be written as \(2^5∗5^2\)
Therefore the number of factors of 800 are (5+1)(2+1) = 6*3 = 18 factors.
Therefore the no. of factors of 9600 which are divisible by 12 are 18 factors in total.
But the question stem asks us how many factors of 9600 are NOT divisible by 12?
Therefore we will have to deduct all the factors of 9600 which are divisible by 12 from all the factors of 9600 to get all the factors of 9600 which are NOT divisible by 12.
9600 can be written as \(2^7∗3*5^2\)
Therefore the number of factors of 9600 are (7+1)(1+1)(2+1) = 8*2*3 = 48 factors.
All the factors of 9600 which are NOT divisible by 12 = 48 factors - 18 factors = 30 factors [hence the correct answer is (B)]
Now 10 is a factor of 800, so is 20, so is 400, including many others.
10, 20 and 400 are not divisible by 12 but (12*10), (12*20) and (12*400) are divisible by 12 because we are multiplying and dividing my 12. Hence every factor of 800 is also a factor of 9600 and is divisible by 12 if we are multiplying each factor of 800 by 12.
To find the number of factors of 800 is a straightforward application of number of factors formula:-
(p+1)(q+1)(r+1)... [where p,q,r are exponents of each prime factor]
Therefore 800 can be written as \(2^5∗5^2\)
Therefore the number of factors of 800 are (5+1)(2+1) = 6*3 = 18 factors.
Therefore the no. of factors of 9600 which are divisible by 12 are 18 factors in total.
But the question stem asks us how many factors of 9600 are NOT divisible by 12?
Therefore we will have to deduct all the factors of 9600 which are divisible by 12 from all the factors of 9600 to get all the factors of 9600 which are NOT divisible by 12.
9600 can be written as \(2^7∗3*5^2\)
Therefore the number of factors of 9600 are (7+1)(1+1)(2+1) = 8*2*3 = 48 factors.
All the factors of 9600 which are NOT divisible by 12 = 48 factors - 18 factors = 30 factors [hence the correct answer is (B)]
