Find the greatest common factor. 10u^3, 6u^3 Write your answer as a constant times a product of single variables raised to exponents. ______

Factorization of 10u^3: First, we need to find the complete factorization of 10u^3. 10 = 2 * 5 u^3 = u * u * u Therefore, 10u^3 = 2 * 5 * u * u * uFactorization of 6u^3: Next, we find the complete factorization of 6u^3. 6 = 2 * 3 u^3 = u * u * u So, 6u^3 = 2 * 3 * u * u * uComparison of Factorizations: Now, we compare the factorizations to find the common factors: 10u^3 = 2 * 5 * u * u * u 6u^3 = 2 * 3 * u * u * u The common factors are 2, u, u, and u.Calculation of GCF: Multiplying the common factors together gives us the greatest common factor (GCF): GCF = 2 * u * u * u = 2u^3

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Math Problems

Algebra 1

GCF of monomials

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Q. Find the greatest common factor.

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10u^3, 6u^3

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

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Factorization of $10u^3$ : First, we need to find the complete factorization of $10u^3$ . $\newline$ $10 = 2 \times 5$ $\newline$ $u^3 = u \times u \times u$ $\newline$ Therefore, $10u^3 = 2 \times 5 \times u \times u \times u$
Factorization of $6u^3$ : Next, we find the complete factorization of $6u^3$ . $\newline$ $6 = 2 \times 3$ $\newline$ $u^3 = u \times u \times u$ $\newline$ So, $6u^3 = 2 \times 3 \times u \times u \times u$
Comparison of Factorizations: Now, we compare the factorizations to find the common factors: $\newline$ $10u^3 = 2 \times 5 \times u \times u \times u$ $\newline$ $6u^3 = 2 \times 3 \times u \times u \times u$ $\newline$ The common factors are $2$ , $u$ , $u$ , and $u$ .
Calculation of GCF: Multiplying the common factors together gives us the greatest common factor (GCF): $\text{GCF} = 2 \times u \times u \times u = 2u^3$