Question

What is the greatest common factor of 48 and 30?

Answer 1

To find the greatest common factor (GCF) of 48 and 30, we can use the prime factorization method.

1. **Prime Factorization of 48:**
- 48 can be divided by 2: \( 48 \div 2 = 24 \)
- 24 can be divided by 2: \( 24 \div 2 = 12 \)
- 12 can be divided by 2: \( 12 \div 2 = 6 \)
- 6 can be divided by 2: \( 6 \div 2 = 3 \)
- 3 is a prime number.

Thus, the prime factorization of 48 is:
\[
48 = 2^4 \times 3^1
\]

2. **Prime Factorization of 30:**
- 30 can be divided by 2: \( 30 \div 2 = 15 \)
- 15 can be divided by 3: \( 15 \div 3 = 5 \)
- 5 is a prime number.

Thus, the prime factorization of 30 is:
\[
30 = 2^1 \times 3^1 \times 5^1
\]

3. **Finding the GCF:**
To find the GCF, we take the lowest power of each common prime factor from both factorizations:
- The common prime factors are 2 and 3.
- For 2: the minimum power is \( 2^1 \).
- For 3: the minimum power is \( 3^1 \).

Therefore, the GCF is:
\[
GCF = 2^1 \times 3^1 = 2 \times 3 = 6
\]

Thus, the greatest common factor of 48 and 30 is \( \boxed{6} \).