Questions: Find the greatest common factor of 25x^4 and 20a^2.

Find the greatest common factor of 25x^4 and 20a^2.
Transcript text: Find the greatest common factor of $25 x^{4}$ and $20 a^{2}$.
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Solution

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Solution Steps

Step 1: Factorize the coefficients
  • The coefficients of the terms are 25 and 20.
  • Factorize 25: \( 25 = 5^2 \)
  • Factorize 20: \( 20 = 2^2 \times 5 \)
Step 2: Identify the common factors of the coefficients
  • The common factor of 25 and 20 is \( 5 \).
Step 3: Identify the common variable factors
  • The variable factors are \( x^4 \) and \( a^2 \).
  • Since there are no common variables between \( x^4 \) and \( a^2 \), the common variable factor is 1.

Final Answer

The greatest common factor (GCF) of \( 25x^4 \) and \( 20a^2 \) is \( 5 \).

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