Question

How do you find the GCF of \[16x,24{{x}^{2}}\]?

Answer 1

Hint: In this problem, we have to find the Greatest common factor for the given terms. We know that Greatest common factor (GCF) of a set of numbers is the largest number that is the factor of all those numbers. Here we can first split the terms into its prime factor and find the largest common number, which is the Greatest common factor of the given terms.

Complete step by step solution:
We know that the given terms are,
\[16x,24{{x}^{2}}\]
We also know that Greatest common factor (GCF) of a set of numbers is the largest number that is the factor of all those numbers.
Now we can find the Greatest common factor for \[16x,24{{x}^{2}}\].
We can now write the first term as,
\[\Rightarrow 16x=4\times 4\times x\]…… (1)
We can now write the second term as,
\[\Rightarrow 24{{x}^{2}}=6\times 4\times x\times x\] ……. (2)
 We can now compare (1) and (2), we can see that these two equations have largest common term which is the Greatest common factor (GCD),
\[\Rightarrow 4x\]
Therefore, the Greatest common factor (GCD) of \[16x,24{{x}^{2}}\] is 4x.

Note: We should always remember that the Greatest common factor is the largest common term of any two numbers, which we can get from its multiples. We should break down every term into prime factors to determine the greatest common factor. We can also note that if there are no common prime factors, then Greatest common factor is 1.