What is the GCF of 18 and 24?
Understand the Problem
The question is asking for the greatest common factor (GCF) of the numbers 18 and 24. To find the GCF, we will identify the largest number that divides both 18 and 24 without leaving a remainder.
Answer
6
Answer for screen readers
The final answer is 6
Steps to Solve
- Find the prime factors of each number
Start by finding the prime factors of 18 and 24.
- Prime factors of 18: $18 = 2 \times 3^2$
- Prime factors of 24: $24 = 2^3 \times 3$
- Identify the common prime factors
Next, identify the common prime factors in both factorizations.
- Common factors: 2 and 3
- Determine the lowest powers of the common prime factors
Choose the lowest power of each common prime factor.
- The lowest power of 2 is $2^1$
- The lowest power of 3 is $3^1$
- Multiply the lowest powers of the common prime factors
Multiply these lowest powers to find the GCF.
$$2^1 \times 3^1 = 2 \times 3 = 6$$
The final answer is 6
More Information
The greatest common factor (GCF) is the largest number that can evenly divide both numbers without leaving a remainder. It's useful in simplifying fractions, among other applications.
Tips
A common mistake is not properly identifying and using the lowest powers of the common prime factors. Ensuring that you multiply the smallest powers is crucial in finding the correct GCF.
