34. Using prime factorization, what is the greatest common factor of the square root of 196 and the square root of 49?
Answer: B
The greatest common factor of the square root of 196 and the square root of 49 is 7.
The square root of 196 is 14 and the square root of 49 is 7. The greatest common factor (GCF) of these two numbers is 7.
A) 4
Option A is incorrect because 4 is not a factor of both 14 and 7. The factors of 14 are 1, 2, 7, and 14, while the factors of 7 are 1 and 7. Since 4 does not appear in either list, it cannot be the GCF.
B) 7
Option B is correct as the GCF of 14 and 7 is indeed 7. Both numbers share 7 as a common factor, and it is the highest number that divides both without leaving a remainder.
C) 14
Option C is incorrect because, while 14 is a factor of itself, it is not a factor of 7. Therefore, it cannot be the GCF since GCF must be a common factor of both numbers.
D) 49
Option D is incorrect because 49 is not a factor of either 14 or 7. Therefore, it cannot be the GCF as it does not divide evenly into both numbers.
Conclusion
The correct answer is 7 because it is the largest number that divides both 14 and 7 without a remainder. All other options fail to meet the requirement of being a common factor for both numbers, as they either do not divide evenly or are not common to both.