what is the GCF of 3 and 18
The Correct Answer and Explanation is:
The Greatest Common Factor (GCF) of 3 and 18 is 3.
Explanation:
To find the GCF of two numbers means to determine the largest number that divides both numbers exactly, with no remainder.
Step 1: Understand the definition of GCF
The GCF (Greatest Common Factor) is the greatest number that evenly divides two or more numbers. This number must be a factor of both original numbers.
Step 2: List the factors of each number
- Factors of 3:
A factor is a number that divides evenly into another number.
The factors of 3 are: 1, 3 - Factors of 18:
The numbers that divide 18 without a remainder are:
1, 2, 3, 6, 9, 18
Step 3: Identify common factors
Now, compare the factors of 3 and 18:
- Common factors of 3 and 18: 1, 3
Step 4: Choose the greatest common factor
From the list above, the largest factor that both numbers share is 3.
So, the GCF of 3 and 18 is 3.
Why is the GCF important?
The GCF is used in many areas of mathematics, such as:
- Reducing fractions: To simplify a fraction, divide both the numerator and denominator by their GCF.
- Factoring expressions: In algebra, factoring out the GCF makes expressions easier to work with.
- Problem-solving: The GCF helps solve problems involving ratios, division of items into equal groups, and more.
Shortcut Method: Prime Factorization
- Prime factorization of 3: 3
- Prime factorization of 18: 2 × 3 × 3
The only prime factor they both share is 3. So, the GCF is 3.
Final Answer:
The GCF of 3 and 18 is 3.
