Question

What is the greatest common factor of 18 and 42?

Answer 1

To find the greatest common factor (GCF) of 18 and 42, we first determine the prime factorization of each number.

**Prime factorization of 18:**
- 18 can be divided by 2:
\( 18 \div 2 = 9 \)
- Then, 9 can be divided by 3:
\( 9 \div 3 = 3 \)
- Finally, 3 can be divided by 3:
\( 3 \div 3 = 1 \)

Thus, the prime factorization of 18 is:
\( 18 = 2 \times 3^2 \)

**Prime factorization of 42:**
- 42 can be divided by 2:
\( 42 \div 2 = 21 \)
- Then, 21 can be divided by 3:
\( 21 \div 3 = 7 \)
- Lastly, 7 is a prime number and cannot be divided further.

Thus, the prime factorization of 42 is:
\( 42 = 2 \times 3 \times 7 \)

**Finding the GCF:**
Next, we identify the common prime factors and their lowest powers in both factorizations.
- The common prime factors of 18 and 42 are:
- 2 (minimum power is \( 2^1 \))
- 3 (minimum power is \( 3^1 \))

Now, we multiply the common prime factors:
\( \text{GCF} = 2^1 \times 3^1 = 2 \times 3 = 6 \)

Therefore, the greatest common factor of 18 and 42 is \( \boxed{6} \).