Final answer:
To find the GCF of 100 and 48, we perform prime factorization of both numbers and identify the common prime factors. The GCF is 2², which is equal to 4.
Step-by-step explanation:
The greatest common factor (GCF) of two numbers can be found using prime factorization. To find the GCF of 100 and 48, we'll factor both numbers into their prime factors.
The common prime factors are 2² since that is the highest power of 2 that both numbers have in common. There are no other common prime factors, as 100 has the prime number 5 and 48 has the prime number 3, which do not match.
Therefore, the GCF of 100 and 48 is 2², which is 4. This GCF can be used for simplifying fractions or for finding out if the numbers can be divided by certain divisors evenly.