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C
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Difficulty:
55%
(hard)
Question Stats:
64% (01:56) correct
36%
(01:56)
wrong
based on 762
sessions
History
Date
Time
Result
Not Attempted Yet
How many distinct positive factors does 30,030 have?
A. 16
B. 32
C. 64
D. 128
E. 256
A. 16
B. 32
C. 64
D. 128
E. 256
18 Dec 2012, 04:30
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Bookmarks
Drik
How many distinct positive factors does 30,030 have?
A. 16
B. 32
C. 64
D. 128
E. 256
A. 16
B. 32
C. 64
D. 128
E. 256
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.
BACK OT THE ORIGINAL QUESTION:
Factorize 30,030=2*3*5*7*11*13, thus the number of factors of 30,030 is (1+1)(1+1)(1+1)(1+1)(1+1)(1+1)=2^6=64.
Answer: C.
P.S. Please read carefully and follow: rules-for-posting-please-read-this-before-posting-133935.html Pay attention to the rules #2 and 7. Thank you.
General Discussion
19 Nov 2015, 13:38
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Bunuel
Factorize 30,030=2*3*5*7*11*13, thus the number of factors of 30,030 is (1+1)(1+1)(1+1)(1+1)(1+1)(1+1)=2^6=64.
How does one do this aspect quickly?
