Use prime factorizations to find GCF and LCM of 28, 49, and 63

Sure, let's start by finding the prime factorizations of the three numbers.

1. Prime factorization of 28: 2^2 * 7^1
2. Prime factorization of 49: 7^2
3. Prime factorization of 63: 3^2 * 7^1

Now, to find the Greatest Common Factor (GCF), we take the lowest power of each prime number common to all three numbers. In this case, the only prime number common to all three numbers is 7, and the lowest power is 7^1. So, the GCF is 7^1 = 7.

To find the Least Common Multiple (LCM), we take the highest power of each prime number in the factorizations. The prime numbers are 2, 3, and 7. The highest power of 2 is 2^2, the highest power of 3 is 3^2, and the highest power of 7 is 7^2. So, the LCM is 2^2 * 3^2 * 7^2 = 4 * 9 * 49 = 1764.