What is the greatest common factor of 40 and 63
The correct answer and explanation is:
Correct Answer: 1
Explanation:
To find the greatest common factor (GCF) of two numbers, we look for the largest number that evenly divides both numbers.
Let’s examine the steps to find the GCF of 40 and 63:
Step 1: Prime Factorization
40
Prime factorization:
40 = 2 × 2 × 2 × 5 = 2³ × 5
63
Prime factorization:
63 = 3 × 3 × 7 = 3² × 7
Step 2: Identify Common Prime Factors
Now compare the prime factorizations:
- 40 = 2³ × 5
- 63 = 3² × 7
They share no common prime factors. This means they do not have any number (other than 1) that divides both.
Step 3: Determine the GCF
Since they have no common prime factors, the greatest common factor is:
👉 1
This means 40 and 63 are relatively prime, or coprime, because they do not have any common divisor other than 1.
Why This Is Important
Understanding the GCF is useful in:
- Simplifying fractions: If you have the fraction 40/63, the GCF helps you reduce it to its lowest terms (in this case, it is already simplified).
- Solving problems in ratios and proportions.
- Working with least common multiples (LCM), where knowing the GCF can help.
Conclusion
The greatest common factor of 40 and 63 is 1, because they do not share any prime factors. This tells us that the two numbers are coprime and do not have any larger common divisors.