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14 Apr 2020, 04:21
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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:
45%
(medium)
Question Stats:
67% (02:14) correct
33%
(02:12)
wrong
based on 152
sessions
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How many positive factors of \(2^6*5^5*7^6*10^7\) are even numbers?
A. 1200
B. 1183
C. 1050
D. 900
E. 840
Are You Up For the Challenge: 700 Level Questions
A. 1200
B. 1183
C. 1050
D. 900
E. 840
Are You Up For the Challenge: 700 Level Questions
14 Apr 2020, 04:29
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Bunuel
Concept:Total Factors - Odd factors = Even factors
For ODD factors we need to exclude all powers of 2
For ODD factors we need to exclude all powers of 2
i.e. Odd factors of \(2^6*5^5*7^6*10^7 = 2^{13}*5^{12}*7^6\) will be formed by only considering the factors of \(5^{12}*7^6\)
If \(N = a^p*b^q*c^r...\)
where a, b, c... are distinct primes
Number of factors of \(N = (p+1)*(q+1)*(r+1)*...\)
where a, b, c... are distinct primes
Number of factors of \(N = (p+1)*(q+1)*(r+1)*...\)
Factors of \(5^{12}*7^6\) will be \((12+1)*(6+1) = 91\)
Total Factors of \(2^{13}*5^{12}*7^6\) will be (13+1)*(12+1)*(6+1) = 1274
Even factors = 1274 - 91 = 1183
Answer: Option B
To know the derivation of Property of ways of finding factors of a number is available in th video here
14 Apr 2020, 07:33
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given value
\(2^6*5^5*7^6*10^7\) can be written as
2^6*2^7* 5^12* 7^6
=> 2^13* 5^12*7^6
so total odd factors ; ( 5^12* 7^6 ) ; ( 13*7) ; 91
and total possible factors ; ( 2^13*5^12*7^6) ; ( 14*13*7) ; 1274
so exactly even numbers ; 1274-91 ; 1183
OPTION B
\(2^6*5^5*7^6*10^7\) can be written as
2^6*2^7* 5^12* 7^6
=> 2^13* 5^12*7^6
so total odd factors ; ( 5^12* 7^6 ) ; ( 13*7) ; 91
and total possible factors ; ( 2^13*5^12*7^6) ; ( 14*13*7) ; 1274
so exactly even numbers ; 1274-91 ; 1183
OPTION B
Bunuel
