What is the greatest common factor of 18 and 35?
Understand the Problem
The question is asking to find the greatest common factor (GCF) of the numbers 18 and 35. The GCF is the largest positive integer that divides both numbers without leaving a remainder. To solve this, we will need to identify the factors of each number and determine the highest one they share.
Answer
The GCF of 18 and 35 is $1$.
Answer for screen readers
The greatest common factor (GCF) of 18 and 35 is $1$.
Steps to Solve
- Identify the factors of 18
To find the factors of 18, we list the numbers that can multiply to give 18:
The factors of 18 are: 1, 2, 3, 6, 9, and 18.
- Identify the factors of 35
Next, we list the factors of 35, which are the numbers that can multiply to give 35:
The factors of 35 are: 1, 5, 7, and 35.
- Determine the common factors
Now we will find the factors that are common to both lists:
Common factors of 18 and 35: 1.
- Identify the greatest common factor (GCF)
Among the common factors identified, the largest one is the greatest common factor:
So, the GCF of 18 and 35 is: 1.
The greatest common factor (GCF) of 18 and 35 is $1$.
More Information
The number $1$ is known as the trivial factor, as it is the only number that is a factor of every integer. This means that 18 and 35 are co-prime numbers, which implies there are no other common factors apart from $1$.
Tips
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Overlooking common factors: Sometimes people might miss out on recognizing that $1$ is a common factor. Remember to always include $1$ when listing factors.
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Confusing GCF with LCM: It's easy to confuse greatest common factor with least common multiple. Ensure you understand the difference between these two concepts.
