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Prime factors

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SVP
Joined: 26 Mar 2013
Posts: 2133

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03 Sep 2017, 11:17
Dear mikemcgarry

I hope you are well.

I need your help in understanding 2 terminologies in prime factors.

What is the difference between 'Number of prime factors and Number of unique prime factors'

How can we apply those concepts in numbers such as 12 & 25??

Thanks in advance for you support
Magoosh GMAT Instructor
Joined: 28 Dec 2011
Posts: 4485

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03 Sep 2017, 15:28
1
Mo2men wrote:
Dear mikemcgarry

I hope you are well.

I need your help in understanding 2 terminologies in prime factors.

What is the difference between 'Number of prime factors and Number of unique prime factors'

How can we apply those concepts in numbers such as 12 & 25??

Thanks in advance for you support

Dear Mo2men,

My friend, good to hear from you! I hope you're well! I'm happy to respond.

First, let's look at the the prime factorizations, which I am sure you understand.
12 = 2*2*3
25 = 5*5
36 = 2*2*3*3
Here, 12 has 3 prime factors, 25 has 2 prime factors, and 36 has 4 prime factors. Sometimes, for clarity, this is called the "total number of prime factors." Of course, 36 needs a product of all four of those factors, both 2's and both 3's, to be 36.

We start talking about something very different when we discuss the "number of unique prime factors" or the "number of distinct prime factors" (the GMAT could use either terminology). Here, we want to know how many different prime factors divide into the number.
12 has two distinct prime factors: 2 and 3
25 has just one distinct prime factor: 5
36 has two distinct prime factors: 2 and 3
In fact, we could look at all the products of powers of 2 and powers of 3 (e.g. 72, 96, 144, 288, 324, 1296) also have just two distinct prime factors.

Does this make sense?
Mike
_________________
Mike McGarry
Magoosh Test Prep

Education is not the filling of a pail, but the lighting of a fire. — William Butler Yeats (1865 – 1939)
SVP
Joined: 26 Mar 2013
Posts: 2133

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03 Sep 2017, 16:36
mikemcgarry wrote:
Mo2men wrote:
Dear mikemcgarry

I hope you are well.

I need your help in understanding 2 terminologies in prime factors.

What is the difference between 'Number of prime factors and Number of unique prime factors'

How can we apply those concepts in numbers such as 12 & 25??

Thanks in advance for you support

Dear Mo2men,

My friend, good to hear from you! I hope you're well! I'm happy to respond.

First, let's look at the the prime factorizations, which I am sure you understand.
12 = 2*2*3
25 = 5*5
36 = 2*2*3*3
Here, 12 has 3 prime factors, 25 has 2 prime factors, and 36 has 4 prime factors. Sometimes, for clarity, this is called the "total number of prime factors." Of course, 36 needs a product of all four of those factors, both 2's and both 3's, to be 36.

We start talking about something very different when we discuss the "number of unique prime factors" or the "number of distinct prime factors" (the GMAT could use either terminology). Here, we want to know how many different prime factors divide into the number.
12 has two distinct prime factors: 2 and 3
25 has just one distinct prime factor: 5
36 has two distinct prime factors: 2 and 3
In fact, we could look at all the products of powers of 2 and powers of 3 (e.g. 72, 96, 144, 288, 324, 1296) also have just two distinct prime factors.

Does this make sense?
Mike

Dear Mike,

Thanks a lot for simple awesome explanation
Manager
Joined: 18 Jan 2017
Posts: 128

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03 Sep 2017, 17:00
mikemcgarry wrote:
Mo2men wrote:
Dear mikemcgarry

I hope you are well.

I need your help in understanding 2 terminologies in prime factors.

What is the difference between 'Number of prime factors and Number of unique prime factors'

How can we apply those concepts in numbers such as 12 & 25??

Thanks in advance for you support

Dear Mo2men,

My friend, good to hear from you! I hope you're well! I'm happy to respond.

First, let's look at the the prime factorizations, which I am sure you understand.
12 = 2*2*3
25 = 5*5
36 = 2*2*3*3
Here, 12 has 3 prime factors, 25 has 2 prime factors, and 36 has 4 prime factors. Sometimes, for clarity, this is called the "total number of prime factors." Of course, 36 needs a product of all four of those factors, both 2's and both 3's, to be 36.

We start talking about something very different when we discuss the "number of unique prime factors" or the "number of distinct prime factors" (the GMAT could use either terminology). Here, we want to know how many different prime factors divide into the number.
12 has two distinct prime factors: 2 and 3
25 has just one distinct prime factor: 5
36 has two distinct prime factors: 2 and 3
In fact, we could look at all the products of powers of 2 and powers of 3 (e.g. 72, 96, 144, 288, 324, 1296) also have just two distinct prime factors.

Does this make sense?
Mike

Who da man? YOU, da man!

Mike, I am a student of Magoosh and I have dedicated next 10 days to complete Quant from our beautiful website. I really like your explanations.
I am sure I will disturb you once I have completed my QUANT module from the portal. I want to have a one on one chat with you (maybe PMs) regarding the 700+ level problems + DS that occur in the GMAT.

Happy Labor's Day. It's your off day today.

Will catch up with you soon.

Regards,
Inder
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Re: Prime factors   [#permalink] 03 Sep 2017, 17:00
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