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What is the greatest common factor of
3x^(4),15x^(3), and
21x^(2) ?

What is the greatest common factor of $3 x^{4}, 15 x^{3}$ , and $21 x^{2}$ ?

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Greatest common factor of three or four numbers

Full solution

Q. What is the greatest common factor of

3 x^{4}, 15 x^{3}

, and

21 x^{2}

?

Factor coefficients: To find the greatest common factor (GCF) of the given algebraic terms $3x^{4}$ , $15x^{3}$ , and $21x^{2}$ , we first need to factor out the coefficients and the variables separately.
Identify common factors: Factor the coefficients $3$ , $15$ , and $21$ . The factors of $3$ are $1$ and $3$ . The factors of $15$ are $1$ , $3$ , $5$ , and $15$ . The factors of $21$ are $1$ , $3$ , $15$ $4$ , and $21$ .
Factor variable part: Identify the common factors of the coefficients. The common factors of $3$ , $15$ , and $21$ are $1$ and $3$ .
Combine common factors: Now, factor the variable part. Since we are looking for the GCF, we take the variable with the smallest exponent, which is $x^{2}$ in this case.
Find GCF: Combine the common factors of the coefficients and the variable part. The GCF of $3x^{4}$ , $15x^{3}$ , and $21x^{2}$ is $3x^{2}$ .

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