Identify the greatest common factor of 66 and 48, z48z.

Answer 1

To find the greatest common factor (GCF) of 66 and 48, we can start by determining the prime factorization of each number.

1. Prime factorization of 66:

   • The prime factors of 66 are \(2 \times 3 \times 11\).

2. Prime factorization of 48:

   • The prime factors of 48 are \(2^4 \times 3\).

Now, we identify the common prime factors from both factorizations:

• From 66, the prime factors are \(2^1\), \(3^1\), and \(11^1\).
• From 48, the prime factors are \(2^4\) and \(3^1\).

The common factors are \(2\) and \(3\).

Now, we take the lowest exponent for each of the common prime factors:

• For \(2\), the lowest exponent is \(1\) (from 66).
• For \(3\), the lowest exponent is \(1\) (from both).

Now, we multiply these together to find the GCF:

\[ GCF = 2^1 \times 3^1 = 2 \times 3 = 6 \]

So, the greatest common factor of 66 and 48 is \(\boxed{6}\).