Answer :

Final answer:

The GCF of 96, 120, and 156 is determined by identifying and multiplying the common prime factors with the smallest exponents, resulting in a GCF of 12.

Explanation:

The subject of the question is finding the Greatest Common Factor (GCF) of the numbers 96, 120, and 156. To determine the GCF of these numbers, we first list the prime factors of each number:

  1. 96 = 2µ × 3
  2. 120 = 2³ × 3 × 5
  3. 156 = 2² × 3 × 13

Next, we identify the common prime factors from each list. The common prime factors for 96, 120, and 156 are 2 and 3. However, the exponent of the prime factor 2 is different in all three numbers. Therefore, we take the smallest exponent of the number 2, which is 2, and for the number 3, which is 1 (since it's the only exponent that appears in all three numbers).

The GCF can be calculated by multiplying these common prime factors with the smallest exponents: 2² × 3 = 12.

Thus, the GCF of 96, 120, and 156 is 12.

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