Final answer:
The greatest common factor (GCF) of 60 and 84 is 12, obtained by multiplying the smallest powers of common prime factors from their prime factorization.
Step-by-step explanation:
The greatest common factor (GCF) of 60 and 84 is a mathematical concept used to find the largest number that can divide both given numbers without leaving a remainder. To calculate the GCF of 60 and 84, you should perform prime factorization for both numbers and then multiply the smallest powers of common prime factors.
For 60, the prime factorization is 2×2×3×5 and for 84 it's 2×2×3×7. The common prime factors are 2×2×3, which we multiply together to get the GCF: 2×2×3 = 12. Therefore, the GCF of 60 and 84 is 12.