Find the greatest common factor. $$ 2 b^{10}, 4 b^{10}, 42 b^{10}, 36 b^{10} $$ Write your answer as a constant times a product of single variables raised to exponents.

Question

UpStudy AI · Accepted Answer

To find the greatest common factor (GCF) of the terms $$ 2b^{10}, 4b^{10}, 42b^{10}, 36b^{10} $$, we will first identify the coefficients and the variable parts separately.

1. **Coefficients**: The coefficients are $$ 2, 4, 42, $$ and $$ 36 $$.
   - The prime factorization of each coefficient is:
     - $$ 2 = 2^1 $$
     - $$ 4 = 2^2 $$
     - $$ 42 = 2^1 \times 3^1 \times 7^1 $$
     - $$ 36 = 2^2 \times 3^2 $$

Now, we find the GCF of the coefficients:
   - The minimum power of $$ 2 $$ among the coefficients is $$ 2^1 $$.
   - The minimum power of $$ 3 $$ is $$ 3^0 $$ (since $$ 2 $$ and $$ 4 $$ do not have $$ 3 $$).
   - The minimum power of $$ 7 $$ is $$ 7^0 $$ (since $$ 2, 4, $$ and $$ 36 $$ do not have $$ 7 $$).

Therefore, the GCF of the coefficients is:
   $$
   2^1 \times 3^0 \times 7^0 = 2
   $$

2. **Variable Part**: All terms have the variable part $$ b^{10} $$. The GCF of $$ b^{10} $$ is simply $$ b^{10} $$.

3. **Combining the GCFs**: Now we combine the GCF of the coefficients and the variable part:
   $$
   \text{GCF} = 2 \cdot b^{10}
   $$

Thus, the greatest common factor of $$ 2b^{10}, 4b^{10}, 42b^{10}, 36b^{10} $$ is:
$$
\boxed{2b^{10}}
$$
The greatest common factor is $$ 2b^{10} $$.

Find the greatest common factor.

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

Upstudy AI Solution

Answer

Solution

Beyond the Answer

Related Questions

Latest Algebra Questions

Find the greatest common factor. Write your answer as a constant times a product of single variables raised to exponents.