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Find the greatest common factor. $\newline$ $10a, 2a^2$ $\newline$ Write your answer as a constant times a product of single variables raised to exponents. $\newline$ $\_\_$

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GCF of monomials

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Q. Find the greatest common factor.

\newline

10a, 2a^2

\newline

Write your answer as a constant times a product of single variables raised to exponents.

\newline

\_\_

Find Prime Factorization: First, we need to find the prime factorization of the first term, $10a$ . $\newline$ $10 = 2 \times 5$ $\newline$ $a = a$ $\newline$ So, $10a = 2 \times 5 \times a$
Compare Factorizations: Next, we find the prime factorization of the second term, $2a^2$ . $\$2 = 2$ \) $\$a^2 = a \times a$ \)So, $2a^2 = 2 \times a \times a$
Calculate Greatest Common Factor: Now, we compare the prime factorizations to find the common factors. $\newline$ For $10a$ : $2 \times 5 \times a$ $\newline$ For $2a^2$ : $2 \times a \times a$ $\newline$ The common factors are $2$ and $a$ .
Calculate Greatest Common Factor: Now, we compare the prime factorizations to find the common factors. $\newline$ For $10a$ : $2 \times 5 \times a$ $\newline$ For $2a^2$ : $2 \times a \times a$ $\newline$ The common factors are $2$ and $a$ .The greatest common factor (GCF) is the product of the common factors. $\newline$ GCF = $2 \times a$

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