Solving for Highest Common Factor (HCF) with 3 Numbers

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To find the highest common factor (HCF) of three numbers, identify the prime factors of each number and determine the common factors. The HCF is the product of the prime factors that all numbers share. If there are no common prime factors, the HCF is 1. For example, the HCF of 12, 6, and 8 is 2, while for 14, 8, and 21, it is 1. Understanding this method allows for the calculation of HCF regardless of the number of integers involved.
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when i come across hcf , i can solve for hcf for 2 numbers, but if the hcf requires 3 ?
do i need to split them ?
 
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Do you mean the "hcf" or "highest common factor" (also called the "greatest common divisor") of three or more numbers? It doesn't really matter how many numbers you have you do the same thing: Find all prime factors of each number and see how many prime factors they all have in common. The "highest common factor" is the product of those prime factors. If they have no prime factors in common, the "highest common factor" is 1.

For example, 12, 6, and 8 factor as 22*3, 2*3, and 23. The last number has no factor of 3. While each has a factor of 2, 6 has only one 2: the highest common factor is 2.

If it were 14= 2*7, 8= 23, and 21= 3*7, since 8 has only 2 as prime factor and 21 does not have a factor of 2, they have no prime factors in common: the highest common factor is 1.
 

Thread 'Greatest possible value of a constant in polynomial'

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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