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C
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
55%
(hard)
Question Stats:
65% (02:08) correct
35%
(02:15)
wrong
based on 516
sessions
History
Date
Time
Result
Not Attempted Yet
Find the number of factors of a three digit even number xyz where x, y and z are distinct prime numbers (2, 3 and 5)
A. 8
B. 10
C. 12
D. 16
E. 24
A. 8
B. 10
C. 12
D. 16
E. 24
04 Mar 2012, 04:57
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kiran882
Since xyz is an even number then it's \(532=2^2*7*19\) or \(352=2^5*11\).
In either case the # of factors is 12:
For \(532=2^2*7*19\) the # of factors will be \((2+1)(1+1)(1+1)=12\);
For \(352=2^5*11\) the # of factors will be \((5+1)(1+1)=12\).
Answer: C.
In case one doesn't know.
Finding the Number of Factors of an Integer
First make prime factorization of an integer \(n=a^p*b^q*c^r\), where \(a\), \(b\), and \(c\) are prime factors of \(n\) and \(p\), \(q\), and \(r\) are their powers.
The number of factors of \(n\) will be expressed by the formula \((p+1)(q+1)(r+1)\). NOTE: this will include 1 and n itself.
Example: Finding the number of all factors of 450: \(450=2^1*3^2*5^2\)
Total number of factors of 450 including 1 and 450 itself is \((1+1)*(2+1)*(2+1)=2*3*3=18\) factors.
For more on number properties check: math-number-theory-88376.html
Hope it helps.
General Discussion
27 Jan 2017, 09:21
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Bunuel
Why answer cannot be E-24. We have 2 even numbers 532 and 352. Both are giving 12 as # of factors. Question asks, Find the number of factors of a three digit even number xyz ? So, Can't we consider both the even numbers ?
