Lesson: Prime Factorization

Comment on Prime Factorization

Are "distinct" prime factors defined as prime factors <10? (looking at some of the reinforcement activity links)
greenlight-admin's picture

"distinct" ≈ "unique"

Example #1: Consider the prime factorization of 88.
88 = (2)(2)(2)(11)
So, the distinct prime factors of 88 are 2 and 11

Example #2:
3042 = (2)(3)(3)(13)(13)
So, the distinct prime factors of 3042 are 2, 3 and 13

Does that help?

Cheers,
Brent

Yes, that does help! I think it was just a coincidence that the questions I saw had distinct prime factors <10. Thank you!!

https://greprepclub.com/forum/s-is-the-set-of-all-integer-multiples-of-2486.html

I'm having trouble understanding the meaning of the sentence of Quantity A. Can you explain to me? Thanks.
greenlight-admin's picture

Question link: https://greprepclub.com/forum/s-is-the-set-of-all-integer-multiples-of-2...

Quantity A: The number of elements in the intersection sets S and T

The intersection of two sets refers to the values that the sets have in common.

For example: set X = {1, 2, 3, 4, 5, 6, 7} and set Y = {2, 4, 6, 8, 10, 12}

The intersection of the sets = 2, 4, 6, because these are the values that both sets have in common.

Does that help?

Cheers,
Brent

7*5=35 is also a divisor of 1540 I'm sure you chose to omit it
greenlight-admin's picture

You're right; 35 is also a divisor of 1540
My intention wasn't to list all of the divisors.

Cheers,
Brent

https://greprepclub.com/forum/if-x-2-7-4-2-7-0-what-is-the-largest-10612.html

I am missing something here, but not sure what. Could you explain to me why we minus one from the powers after factoring?

Factor 2^70 from right side to get: x = 2^70(2^4 - 1)
greenlight-admin's picture

Question link: https://greprepclub.com/forum/if-x-2-7-4-2-7-0-what-is-the-largest-10612...

This is no different from factoring x^74 - x^70
We can factor out x^70 to get: x^74 - x^70 = x^70(x^4 - 1)
Notice that, if we take x^70(x^4 - 1) and expand it, we get back to x^74 - x^70

This kind of factoring is the same as 3x + 3 = 3(x + 1)
Once again, if we expand 3(x + 1), we get back to 3x + 3

It might help to review the lesson on GCF factoring: https://www.greenlighttestprep.com/module/gre-algebra-and-equation-solvi...

Cheers,
Brent

Please direct me to the module of where you taught how to write the Prime factorisation of large numbers
greenlight-admin's picture

The video at the top of the page shows how to find the prime factorization of all numbers.

Cheers,
Brent

I have a question: how many different positive integer factors does 64*81*125 have? this is from kaplan test
greenlight-admin's picture

The strategy for this kind of question is covered here: https://www.greenlighttestprep.com/module/gre-integer-properties/video/828

In the meantime, here's my solution:

For the strategy covered in the video to work, we need only find the prime factorization of the given expression.
(64)(81)(125) = (2)(2)(2)(2)(2)(2)(3)(3)(3)(3)(5)(5)(5)
= (2^6)(3^4)(5^3)

So, the total number of positive factors = (6+1)(4+1)(3+1) = (7)(5)(4) = 140

Cheers,
Brent

Hi Brent,

In this questio : https://greprepclub.com/forum/what-is-the-smallest-positive-integer-that-is-non-prime-10760.html

9!=9*8*7*6*5*4*3*2*1
362880=5*2^7*3^^4*7

so the smallest integer may be evne 11 but ehy didnt you consider 11?

Thanks
greenlight-admin's picture

Question link: https://greprepclub.com/forum/what-is-the-smallest-positive-integer-that...

You're correct to say that 9! = 362,880
However the prime factorization is incorrect.
We know this because 9! = 9 x 8 x 7 x 6 x 5 x 4 x 2 x 1
= (3 x 3) x (2 x 2 x 2) x 7 x (2 x 3) x 5 x (2 x 2) x 2 x 1
= (2⁷)(3³)(5)(7)

Once we know the prime factorization we can see that:
1, 2, 3, 4, 5, 6, 7, 8, and 9 are all factors of 9!
Also, 10 is a factor of 9! since 10 = (5)(2), and we can see one 5 and one 2 hiding in the prime factorization of 9!
Also, 12 is a factor of 9! since 12 = (2)(2)(3), and we can see two 2's and one 3 hiding in the prime factorization of 9!
14 is a factor of 9! since 12 = (2)(7), and we can see one 2's and one 7 hiding in the prime factorization of 9!
16 is a factor of 9! since 16 = (2)(2)(2)(2), and we can see four 2's hiding in the prime factorization of 9!
18 is a factor of 9! since 18 = (2)(3)(3), and we can see one 2 and two 3's hiding in the prime factorization of 9!
20 is a factor of 9! since 12 = (2)(2)(5), and we can see two 2's and one 5 hiding in the prime factorization of 9!
22 is NOT a factor of 9! since 22 = (2)(11), and we there are NO 11's hiding in the prime factorization of 9!

Does that help?

Cheers,
Brent

why are we checking only for some numbers as 22 it means there must be atleast one prime inorder to check with the product so you have not choosen 11
eg : for 18- we have 2's and 3's in as prime factors
but for 11 - we doesnt have 11 or any number such that by multiplying with some x could yeild 18

is this correct
greenlight-admin's picture

The question asked us to find the smallest positive integer that is NON-PRIME and NOT a factor of 9!

Since there are zero 11's hiding in the prime factorization of 9!, we know that 11 is NOT a factor of 9!
However, we're looking for a NON-PRIME that isn't a factor of 9!

So, once I showed that 1, 2, 3, 4, 5, 6, 7, 8, and 9 ARE factors of 9!, I started testing other NON-PRIME values.

So, the next number I chose to examine was 10.
Once I was able to show that 10 IS a factor of 9!, I then tested the NEXT NON-PRIME value (12)
Once I was able to show that 12 IS a factor of 9!, I tested the next NON-PRIME value (14)
Once I was able to show that 14 IS a factor of 9!, I tested the next NON-PRIME value (16)
.
.
.
And so on, until I tested 22

Does that help?

yes, that non prime wrord makes a lot of difference .
Thanks

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