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Answer :
Final answer:
The greatest common factor (GCF) of 30x² and 45x⁵ is 15x³.
Explanation:
The greatest common factor (GCF) of 30x² and 45x⁵ can be found by finding the prime factorization of the two terms and identifying the common factors.
Step 1: Prime factorize 30x² and 45x⁵
- 30 = 2 x 3 x 5
- x² = x x x
- 45 = 3 x 3 x 5
- x⁵ = x x x x x
Step 2: Identify the common factors
- The common prime factors are 3 and 5
- For the variable x, the common factors are x and x
Step 3: Multiply the common factors together
- Common factors for the numbers: 3 x 5 = 15
- Common factors for the variables: x x x = x³
The GCF of 30x² and 45x⁵ is 15x³.
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