What is the GCF of 35 and 56?
Understand the Problem
The question is asking for the greatest common factor (GCF) of the numbers 35 and 56. To find the GCF, we will identify the factors of each number and determine the largest factor that they have in common.
Answer
The greatest common factor of 35 and 56 is $7$.
Answer for screen readers
The greatest common factor of 35 and 56 is $7$.
Steps to Solve
- List the factors of each number
First, we will find the factors of both numbers:
- The factors of $35$ are: $1, 5, 7, 35$.
- The factors of $56$ are: $1, 2, 4, 7, 8, 14, 28, 56$.
- Identify the common factors
Next, we look for common factors between the two lists we created:
- Common factors of $35$ and $56$ are: $1$ and $7$.
- Determine the greatest common factor
Now, we take the largest number from the common factors:
- The greatest common factor (GCF) is $7$.
The greatest common factor of 35 and 56 is $7$.
More Information
The greatest common factor (GCF) is used in various mathematical applications, such as simplifying fractions and finding least common multiples. The GCF helps in understanding the divisibility and relationships between numbers.
Tips
One common mistake is forgetting to list all factors or miscounting them. Also, some may overlook that the GCF is the largest value from the common factors, rather than just any common factor. To avoid these mistakes, it's essential to carefully list and compare all factors.
