Find the greatest common factor of 12 and 42 .

To find the greatest common factor (GCF) of 12 and 42, we start by listing the factors of each number. The factors of 12 are 1, 2, 3, 4, 6, and 12. The factors of 42 are 1, 2, 3, 6, 7, 14, 21, and 42. The common factors are 1, 2, 3, and 6. Out of these, the greatest is 6. Therefore, the GCF of 12 and 42 is 6.

Understanding the GCF is super helpful in simplifying fractions and finding common denominators! For example, if you have the fraction 12/42, dividing both the numerator and the denominator by their GCF of 6 simplifies it to 2/7. Who knew math could be such a time-saver?

To make finding the GCF even easier in the future, you can use the prime factorization method. Break down 12 into its prime factors: 2 × 2 × 3 (or 2² × 3) and 42 into 2 × 3 × 7. The common prime factors are 2 and 3, and multiplying these together (2 × 3) gives you the GCF of 6. Keep this strategy in your back pocket for when you need it!