Factors of 4ab: List and Examples | Homework Help

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The discussion focuses on identifying the various factors of the expression 4ab. Participants list factors such as 4, ab, a, 4b, b, 4a, 2, 2ab, 2b, and 2a. The inclusion of 1 as a factor is confirmed, emphasizing that if a and b are primes, all listed factors are positive integers. The conversation highlights the importance of considering prime variables in factorization. Overall, the thread effectively clarifies the complete set of factors for 4ab.
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Homework Statement



Name the various factors of:

4ab

Homework Equations



None

The Attempt at a Solution



4, ab, a, 4b, b, 4a, 2, 2ab, 2b, 2a

Did I miss any?
 
Last edited:
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How about 1? That's a factor.
 


yes you are right, if a and b are primes
 


Nice, thanx!
 


If a and b are primes, then those are all positive integer factors.
 
Since ##px^9+q## is the factor, then ##x^9=\frac{-q}{p}## will be one of the roots. Let ##f(x)=27x^{18}+bx^9+70##, then: $$27\left(\frac{-q}{p}\right)^2+b\left(\frac{-q}{p}\right)+70=0$$ $$b=27 \frac{q}{p}+70 \frac{p}{q}$$ $$b=\frac{27q^2+70p^2}{pq}$$ From this expression, it looks like there is no greatest value of ##b## because increasing the value of ##p## and ##q## will also increase the value of ##b##. How to find the greatest value of ##b##? Thanks
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