What is the greatest common factor of 35 and 42?
Understand the Problem
The question is asking for the greatest common factor (GCF) of the two numbers 35 and 42. To solve this, we will find the factors of both numbers and identify the largest one they share.
Answer
The GCF of 35 and 42 is $7$.
Answer for screen readers
The greatest common factor of 35 and 42 is $7$.
Steps to Solve
- Find the Factors of 35
To find the factors of 35, we can list the numbers that divide 35 without leaving a remainder. The factors of 35 are: 1, 5, 7, 35.
- Find the Factors of 42
Next, we do the same for 42. The factors of 42 are: 1, 2, 3, 6, 7, 14, 21, 42.
- Identify the Common Factors
Now, we will find the factors that are common to both lists:
- Factors of 35: 1, 5, 7, 35
- Factors of 42: 1, 2, 3, 6, 7, 14, 21, 42
The common factors are 1 and 7.
- Determine the Greatest Common Factor
Finally, we pick the largest number from the common factors. The greatest common factor of 35 and 42 is: $$ GCF = 7 $$
The greatest common factor of 35 and 42 is $7$.
More Information
The greatest common factor (GCF) is the largest number that divides both numbers without leaving a remainder. In this case, 7 is significant since it indicates the largest shared component of the two numbers.
Tips
- Confusing factors with multiples: Ensure that you are identifying factors, not multiples.
- Forgetting to list all factors: Double-check that you've listed all factors for both numbers before concluding.
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