What is the greatest common factor of 35 and 49?
Understand the Problem
The question is asking for the greatest common factor (GCF) of the numbers 35 and 49, which involves identifying the largest number that divides both 35 and 49 without leaving a remainder.
Answer
The GCF of 35 and 49 is $7$.
Answer for screen readers
The greatest common factor (GCF) of 35 and 49 is $7$.
Steps to Solve
- List the factors of each number
First, we will find all the factors of 35 and 49.
- The factors of 35 are: 1, 5, 7, 35
- The factors of 49 are: 1, 7, 49
- Identify the common factors
Next, we determine which factors are common to both sets derived above.
- The common factors of 35 and 49 are: 1, 7
- Find the greatest common factor
Now, we will select the largest factor from the common factors identified in the previous step.
The greatest common factor (GCF) is: 7
The greatest common factor (GCF) of 35 and 49 is $7$.
More Information
The GCF is useful for simplifying fractions, finding common denominators, and solving problems related to divisibility. Identifying the GCF can also help in understanding the relationships between numbers.
Tips
Common mistakes include:
- Overlooking factors or listing them incorrectly.
- Confusing greatest common factor with least common multiple (LCM).
To avoid these mistakes, ensure to carefully list all factors and double-check for commonalities.
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