Find The greatest common factor (GCF) for 63.
The Correct answer and Explanation is:
To find the greatest common factor (GCF) of the number 63, we first need to understand what GCF means. The GCF of two or more integers is the largest positive integer that divides each of the integers without leaving a remainder. In the case of a single number, the GCF is simply the number itself when considering the GCF of its factors.
Step 1: Finding the Factors of 63
The first step is to determine the factors of 63. A factor is a whole number that can be multiplied by another whole number to get the original number. The factors of 63 are:
- Start with 1: 1×63=631 \times 63 = 631×63=63
- Next, check 2: 63 is odd, so it’s not divisible by 2.
- Check 3: 3×21=633 \times 21 = 633×21=63
- Check 4: 63 is not divisible by 4.
- Check 5: 63 does not end in 0 or 5, so it’s not divisible by 5.
- Check 6: 63 is not divisible by 6.
- Check 7: 7×9=637 \times 9 = 637×9=63
- Check 8: 63 is not divisible by 8.
- Check 9: 9×7=639 \times 7 = 639×7=63
Thus, the complete list of factors of 63 is:
- 1
- 3
- 7
- 9
- 21
- 63
Step 2: Identifying the GCF
When considering just the number 63, the greatest common factor of its factors is itself. However, if you were to find the GCF of 63 with another number, you would look for the largest factor that both numbers share.
Conclusion
The GCF of 63, when considered on its own, is 63. If comparing 63 with another number, such as 9, the GCF would be determined based on their common factors (which would still include 9 in this example).
In summary, understanding how to find the GCF involves identifying factors, and recognizing that for a single number, the GCF is simply that number. In the case of 63, the GCF is 63.