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 \( \boxed{6} \).
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