What is the greatest common factor of 48 and 40?
Understand the Problem
The question is asking for the greatest common factor (GCF) between the numbers 48 and 40, which involves identifying the highest number that divides both 48 and 40 without leaving a remainder.
Answer
The greatest common factor of 48 and 40 is $8$.
Answer for screen readers
The greatest common factor of 48 and 40 is $8$.
Steps to Solve
- Find the prime factors of both numbers
To determine the greatest common factor (GCF), start by finding the prime factorization of each number.
-
For 48:
- $48 = 2^4 \times 3^1$
-
For 40:
- $40 = 2^3 \times 5^1$
- List the common prime factors
Next, identify the common prime factors from the factorizations of both numbers.
- The prime factor common to both 48 and 40 is 2.
- Determine the lowest power of the common factors
Now, find the lowest power of the common prime factors.
- The common factor is 2.
- The power of 2 in 48 is 4.
- The power of 2 in 40 is 3.
- The minimum power is 3.
- Calculate the GCF
Finally, calculate the GCF by using the lowest power of the common factors.
- Thus, the GCF is:
$$ GCF = 2^3 = 8 $$
The greatest common factor of 48 and 40 is $8$.
More Information
The GCF is the largest number that divides both 48 and 40 without leaving a remainder. It is useful for simplifying fractions and finding common denominators.
Tips
- Forgetting to check for all prime factors: Ensure all prime factors are considered.
- Incorrectly using the highest powers instead of the lowest: Remember to use the minimum power for the GCF.
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