What is the GCF of 35 and 42?
Understand the Problem
The question is asking for the greatest common factor (GCF) of the numbers 35 and 42. The GCF is the largest positive integer that divides both numbers without leaving a remainder. To find the GCF, we can list the factors of each number and identify the greatest one they have in common.
Answer
The GCF is 7.
Answer for screen readers
The greatest common factor of 35 and 42 is 7.
Steps to Solve
- List the factors of 35
Start by finding all the factors of the number 35. The factors are the numbers that multiply together to give 35.
The factors of 35 are: 1, 5, 7, 35.
- List the factors of 42
Now, find all the factors of the number 42.
The factors of 42 are: 1, 2, 3, 6, 7, 14, 21, 42.
- Identify the common factors
Look for the numbers that are present in both lists of factors.
The common factors of 35 and 42 are: 1, 7.
- Find the greatest common factor
Determine the largest number among the common factors.
The greatest common factor (GCF) is 7.
The greatest common factor of 35 and 42 is 7.
More Information
The greatest common factor is useful in simplifying fractions, finding common denominators, and solving problems that involve divisibility. Additionally, using the GCF helps in factoring polynomials and ratios.
Tips
- Not listing all factors: Ensure all factors are accounted for to avoid missing the GCF.
- Confusing GCF with least common multiple (LCM): Remember that GCF is the largest factor while LCM is the smallest multiple.
