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Re: How many distinct positive factors does 30,030 have? [#permalink]

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18 Dec 2012, 04:30

1

This post received KUDOS

Expert's post

Drik wrote:

How many distinct positive factors does 30,030 have?

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.

Re: How many distinct positive factors does 30,030 have? [#permalink]

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08 Feb 2015, 19:27

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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Brent Hanneson - Founder of GMAT Prep Now, a free & comprehensive GMAT course with: - over 500 videos (35 hours of instruction) - over 800 practice questions - 2 full-length practice tests and other bonus offers - http://www.gmatprepnow.com/

I appreciate the videos which were informative however they don't really answer my specific question; I'm not asking about how to find the # of divisors, I'm wondering how (and this wasn't explained in either video) you quickly figure our the prime factors of a massive number like 30,030?

In the video the question is 14,000 and he just skips to "and here are the prime factors" and I don't get how you figure that out in a timely manner. _________________

I appreciate the videos which were informative however they don't really answer my specific question; I'm not asking about how to find the # of divisors, I'm wondering how (and this wasn't explained in either video) you quickly figure our the prime factors of a massive number like 30,030?

In the video the question is 14,000 and he just skips to "and here are the prime factors" and I don't get how you figure that out in a timely manner.

Brent Hanneson - Founder of GMAT Prep Now, a free & comprehensive GMAT course with: - over 500 videos (35 hours of instruction) - over 800 practice questions - 2 full-length practice tests and other bonus offers - http://www.gmatprepnow.com/

So you see 14,000 and have to do a factor tree starting with a number you can eyeball like 140 and 100 then continue breaking those numbers down?

I'm sorry if I'm missing something here (feel like I'm definitely overcomplicating or simply not getting a simple idea); but when I see a number like 30,030 and one of the steps is "30,030 = 2*3*5*7*11*13" it seems like I'm missing an entire part of the explanation because it seems the speed people are getting these primes would be something more streamlined than a factor tree. It's possible it's just a matter of practice makes it faster I just wasn't sure if I was missing an entire step.

So you see 14,000 and have to do a factor tree starting with a number you can eyeball like 140 and 100 then continue breaking those numbers down?

I'm sorry if I'm missing something here (feel like I'm definitely overcomplicating or simply not getting a simple idea); but when I see a number like 30,030 and one of the steps is "30,030 = 2*3*5*7*11*13" it seems like I'm missing an entire part of the explanation because it seems the speed people are getting these primes would be something more streamlined than a factor tree. It's possible it's just a matter of practice makes it faster I just wasn't sure if I was missing an entire step.

Thank you for the explanations.

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: http://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 _________________

Brent Hanneson - Founder of GMAT Prep Now, a free & comprehensive GMAT course with: - over 500 videos (35 hours of instruction) - over 800 practice questions - 2 full-length practice tests and other bonus offers - http://www.gmatprepnow.com/

How many distinct positive factors does 30,030 have? [#permalink]

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20 Nov 2015, 08:40

GMATPrepNow wrote:

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: http://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

Thank you very much for breaking it down like this, it was a simple matter of the task appearing more daunting to me than it actually was so this step-by-step was perfect thank you Brent. _________________

Re: How many distinct positive factors does 30,030 have? [#permalink]

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16 Mar 2016, 01:15

Here 1001 is divisible by 11 thats the only basic problem to be solved actually and also the number of +ve divisors = product of powers of primes after increase them by 1

gmatclubot

Re: How many distinct positive factors does 30,030 have?
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16 Mar 2016, 01:15

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