What is the greatest common factor of 12, 28, and 4?

1 answer

To find the greatest common factor (GCF) of the numbers 12, 28, and 4, we can start by determining the prime factorization of each number.

  1. Prime Factorization:

    • \( 12 = 2^2 \times 3 \)
    • \( 28 = 2^2 \times 7 \)
    • \( 4 = 2^2 \)
  2. Identifying Common Factors: The common prime factors among these numbers are \( 2 \). To find the GCF, we take the lowest power of the common prime factors.

    The common factor \( 2 \) appears in each factorization with the exponent \( 2 \):

    • For \( 12 \): \( 2^2 \)
    • For \( 28 \): \( 2^2 \)
    • For \( 4 \): \( 2^2 \)
  3. Calculating the GCF: Therefore, the GCF is: \[ 2^2 = 4 \]

Thus, the greatest common factor of 12, 28, and 4 is \( \boxed{4} \).