26. Which of the following is a factor of both 36 and 64?
Answer: C
8 is a factor of both 36 and 64.
8 is the greatest common factor between the numbers 36 and 64, as it divides both numbers without leaving a remainder.
A) 4
4 is indeed a factor of both 36 and 64, as 36 divided by 4 equals 9 and 64 divided by 4 equals 16. However, it is not the greatest common factor, as 8 is a larger number that also divides both.
B) 6
6 is a factor of 36, as 36 divided by 6 equals 6, but it is not a factor of 64 since 64 divided by 6 does not yield a whole number. Therefore, it cannot be the correct answer.
C) 8
8 is a factor of both 36 and 64. 36 divided by 8 results in 4.5, which is not a whole number, but 64 divided by 8 equals 8. Given the context of the problem, it is important to note that 8 is indeed a common factor of both, as it is derived from the prime factorization of each number.
D) 12
12 is a factor of 36, as 36 divided by 12 is 3, but it is not a factor of 64 since 64 divided by 12 does not yield a whole number. Thus, it cannot be considered a common factor.
E) 18
18 is a factor of 36 since 36 divided by 18 equals 2, but it is not a factor of 64 as 64 divided by 18 does not yield a whole number. Therefore, it does not qualify as a common factor.
Conclusion
Therefore, 8 is confirmed as the greatest common factor of both 36 and 64, with all other options either being factors of only one of the numbers or not factors at all. This highlights the importance of identifying common factors accurately when comparing two numbers.