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C
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Difficulty:
55%
(hard)
Question Stats:
67% (01:57) correct
33%
(01:56)
wrong
based on 919
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
19 Nov 2015, 21:00
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redfield
Start with 30,030
I can see this is divisible by 10.
So, 30,030 = (3003)(10)
Or 30,030 = (3003)(2)(5)
What about 3003?
Well, the sum of the digits is 6, and 6 is divisible by 3, which means 3003 is divisible by 3 (this in an important divisibility rule that's discussed in this free video: https://www.gmatprepnow.com/module/gmat- ... /video/822 )
So, 30,030 = (3)(1001)(2)(5)
This is where it gets a bit tricky since it's hard to see any PRIME divisors of 1001. We know that 2, 3 and 5 don't work. What about 7?
When we check we get: 1001 = (7)(143)
So, 30,030 = (3)(7)(143)(2)(5)
Finally, 143 = ...
So, 30,030 = (3)(7)(11)(13)(2)(5)
Cheers,
Brent
18 Dec 2012, 04:30
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Drik
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.
