What is the Gcf of 30 48 and 60

What is the Gcf of 30 48 and 60

The correct answer and explanation is:

The greatest common factor (GCF) of 30, 48, and 60 is 6.

Explanation:

To find the GCF of multiple numbers, we follow these steps:

1. Prime Factorization:
   First, find the prime factorization of each number.
   • 30:
     30 can be broken down into prime factors as: 30=2×3×530 = 2 \times 3 \times 5
   • 48:
     48 can be broken down into prime factors as: 48=24×348 = 2^4 \times 3
   • 60:
     60 can be broken down into prime factors as: 60=22×3×560 = 2^2 \times 3 \times 5
2. Identify Common Factors:
   Now, identify the common prime factors among all three numbers.
   • For 30, 48, and 60, the common prime factors are 2 and 3.
3. Choose the Lowest Powers of Common Factors:
   The next step is to select the lowest powers of the common prime factors.
   • For 2, the lowest power is 212^1, which comes from 30.
   • For 3, the lowest power is 313^1, which is common in all three numbers.
4. Multiply the Common Factors:
   Multiply the lowest powers of the common factors to get the GCF. GCF=21×31=2×3=6GCF = 2^1 \times 3^1 = 2 \times 3 = 6

Conclusion:

Therefore, the greatest common factor (GCF) of 30, 48, and 60 is 6, as it is the largest number that divides all three without leaving a remainder.