What is the Greatest Common Factor (GCF) of 28 and 42?
a. 4
b. 7
c. 14
d. 12
The correct answer and explanation is:
The correct answer is b. 7.
To find the Greatest Common Factor (GCF) of two numbers, you need to identify the largest number that divides both numbers evenly. The process involves finding the factors of each number and then choosing the greatest one they both share.
Step 1: Find the factors of 28
The factors of 28 are all the numbers that divide evenly into 28. These are:
1, 2, 4, 7, 14, 28.
Step 2: Find the factors of 42
The factors of 42 are:
1, 2, 3, 6, 7, 14, 21, 42.
Step 3: Identify the common factors
The common factors between 28 and 42 are:
1, 2, 7, and 14.
Step 4: Choose the greatest common factor
Out of these common factors, the largest is 7.
Thus, the Greatest Common Factor (GCF) of 28 and 42 is 7. The GCF represents the largest number that can divide both 28 and 42 without leaving a remainder. This process can be applied to any pair of numbers, and the GCF is useful in simplifying fractions, factoring expressions, and solving problems involving divisibility.
This method of finding the GCF is known as listing the factors, but there are also other ways to compute the GCF, such as using the prime factorization method or the Euclidean algorithm.