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Answer :
To find the greatest common factor (GCF) of [tex]\(60x^9\)[/tex] and [tex]\(54x^5\)[/tex], follow these steps:
1. Find the GCF of the coefficients:
- The coefficients are 60 and 54.
- To find the GCF of these numbers, list their prime factorizations:
- [tex]\(60 = 2^2 \cdot 3 \cdot 5\)[/tex]
- [tex]\(54 = 2 \cdot 3^3\)[/tex]
- Identify the common prime factors. The common prime factors are 2 and 3.
- Take the lowest power of each common prime factor:
- For 2: the lowest power is [tex]\(2^1 = 2\)[/tex]
- For 3: the lowest power is [tex]\(3^1 = 3\)[/tex]
- Multiply these together: [tex]\(2 \cdot 3 = 6\)[/tex]
- Therefore, the GCF of 60 and 54 is 6.
2. Find the GCF of the variable terms:
- The variable terms are [tex]\(x^9\)[/tex] and [tex]\(x^5\)[/tex].
- The lowest power of [tex]\(x\)[/tex] that is common to both terms is [tex]\(x^5\)[/tex].
3. Combine these results:
- The GCF of the coefficients is 6.
- The GCF of the variable terms is [tex]\(x^5\)[/tex].
Thus, the greatest common factor (GCF) of [tex]\(60x^9\)[/tex] and [tex]\(54x^5\)[/tex] is [tex]\(6x^5\)[/tex].
Therefore, the answer is [tex]\(6x^5\)[/tex].
1. Find the GCF of the coefficients:
- The coefficients are 60 and 54.
- To find the GCF of these numbers, list their prime factorizations:
- [tex]\(60 = 2^2 \cdot 3 \cdot 5\)[/tex]
- [tex]\(54 = 2 \cdot 3^3\)[/tex]
- Identify the common prime factors. The common prime factors are 2 and 3.
- Take the lowest power of each common prime factor:
- For 2: the lowest power is [tex]\(2^1 = 2\)[/tex]
- For 3: the lowest power is [tex]\(3^1 = 3\)[/tex]
- Multiply these together: [tex]\(2 \cdot 3 = 6\)[/tex]
- Therefore, the GCF of 60 and 54 is 6.
2. Find the GCF of the variable terms:
- The variable terms are [tex]\(x^9\)[/tex] and [tex]\(x^5\)[/tex].
- The lowest power of [tex]\(x\)[/tex] that is common to both terms is [tex]\(x^5\)[/tex].
3. Combine these results:
- The GCF of the coefficients is 6.
- The GCF of the variable terms is [tex]\(x^5\)[/tex].
Thus, the greatest common factor (GCF) of [tex]\(60x^9\)[/tex] and [tex]\(54x^5\)[/tex] is [tex]\(6x^5\)[/tex].
Therefore, the answer is [tex]\(6x^5\)[/tex].
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