What is the greatest common factor of 30 and \( 24 ? \)

To find the greatest common factor (GCF) of 30 and 24, we can start by listing the factors of each number. The factors of 30 are 1, 2, 3, 5, 6, 10, 15, and 30, while the factors of 24 are 1, 2, 3, 4, 6, 8, 12, and 24. The highest number that appears in both lists is 6, so the GCF of 30 and 24 is 6! The process of finding the GCF is like a treasure hunt through numbers, uncovering the commonalities between them. Using methods like prime factorization can break down each number into primes: 30 is \( 2 \times 3 \times 5 \) and 24 is \( 2^3 \times 3 \). The common prime factors (2 and 3) combine to give \( 2^1 \times 3^1 = 6 \), proving there are multiple paths to the same numeric treasure!