NP Question about overlap of prime factors

[Videoorchard]

HI There.

I Have a question on number properties..More precisely on the redundant numbers which are in the factor tree...In the chapter 2 problem set,5th question (PG.53),you have combined all the prime factors of 12(factors are 2,2,3) and 10(factors are 2,5) into one single factor tree i.e 2,2,3,5..i do understand that since 2 is a redundant,you cancelled it out..But on the same problem set in problem 8,even though there we redudant 2's in both the factor of the tree,they were not cancelled/removed from the final set (i.e 2,2,2,2,23,7)...Could you please throw some light on how and when should we cancel out the redundant nos from the factor tree.


Regards,
Manish A.

[tommywallach]

Hey Manish,

You only have to worry about overlap when you have two pieces of information on the SAME variable. In the second question you mention, we have two variables (h and k) so there is no possibility of overlap.

Think of it this way

X is divisible by 4 and 8.

In that case, see how the 4 tells us nothing (because anything that's divisible by 8 is already divisible by 4). This is overlap.

But if x is divisible by 4 and y is divisible by 8, then the smallest xy could be is 32 (i.e. there is no overlap).

Hope that helps!

-t

P.S. Also, please don't make subject lines in all caps. Thanks!

[Videoorchard]

Hello Sir,

thank you so much for taking your time and responding to the question.

So just to confirm on what you said,if we ever had a a variable X with the two factors 8 & 4, Then thier final resultant prime factors would be 2,2,2 (eliminating all redudanct 2's)...Now if there were two seperate variable X and Y,with factors 8 & 4, then thier final resultant prime factors would be 2,2,2,2,2...Am i right?

Regards,
Manish A.

[tommywallach]

That's absolutely right, as long as what you mean is that the PRODUCT of x and y (in the second example) would have those primes.

-t