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------------------------------------------------ What is the greatest common factor for [tex]30x^2[/tex] and [tex]45x^5[/tex]?

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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