What is the GCF of 16 and 56?
Understand the Problem
The question is asking for the greatest common factor (GCF) of the numbers 16 and 56. To find the GCF, we can first list the factors of both numbers and then identify the largest factor that is common to both lists.
Answer
The GCF of 16 and 56 is $8$.
Answer for screen readers
The greatest common factor (GCF) of 16 and 56 is $8$.
Steps to Solve
- List the Factors of Each Number
First, we need to find all the factors of the number 16. The factors of 16 are:
1, 2, 4, 8, 16
Next, we will find the factors of 56. The factors of 56 are:
1, 2, 4, 7, 8, 14, 28, 56
- Identify the Common Factors
Now that we have the lists of factors, we need to identify which factors are common to both numbers.
Factors of 16: 1, 2, 4, 8, 16
Factors of 56: 1, 2, 4, 7, 8, 14, 28, 56
The common factors are:
1, 2, 4, 8
- Find the Greatest Common Factor
The final step is to identify the largest common factor from our list. From 1, 2, 4, 8, the greatest is 8.
The greatest common factor (GCF) of 16 and 56 is $8$.
More Information
The GCF is the highest number that divides both numbers without leaving a remainder. Understanding the GCF is useful in simplifying fractions, solving problems involving divisibility, and finding common terms in algebra.
Tips
- Incorrectly identifying factors: It’s crucial to list all factors accurately. Double-check your lists to make sure no factors are missed.
- Confusing GCF with least common multiple (LCM): Remember, GCF finds the largest common divisor, while LCM finds the smallest common multiple.
