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Find the greatest common factor.\newline2k,102k, 10\newlineWrite your answer as a constant times a product of single variables raised to exponents.\newline__\_\_

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Q. Find the greatest common factor.\newline2k,102k, 10\newlineWrite your answer as a constant times a product of single variables raised to exponents.\newline__\_\_
  1. Find Prime Factorization: First, we need to find the prime factorization of each number.\newlineFor 2k2k, since 22 is already a prime number, the factorization is simply 2k2k.\newlineFor 1010, the prime factorization is 2×52 \times 5.
  2. Compare Common Factors: Now, we compare the prime factorizations to find the common factors. The number 22 is the only common prime factor between 2k2k and 1010.
  3. Determine Greatest Common Factor: Since 22 is the only common factor and there are no variables in common, the greatest common factor (GCF) is just 22.
  4. Write GCF as Constant: We write the GCF as a constant times a product of single variables raised to exponents. In this case, there are no variables in the GCF, so it is simply the constant 22.