Using prime factorization, what is the greatest common factor of the square root of 196 and the square root of 49?

Rationale

7

To find the greatest common factor (GCF) of the square roots of 196 and 49, we first calculate the square roots: √196 = 14 and √49 = 7. The GCF of 14 and 7 is 7, making it the highest factor that divides both numbers.

A (4) YOUR ANSWER

The number 4 is not a factor of either 14 or 7. While 4 is a factor of 196, it does not appear in the prime factorization of 49. Thus, it cannot be the GCF of the numbers derived from the square roots.

B (7) CORRECT

The number 7 is indeed a factor of both 14 and 7, as it divides both numbers evenly. Therefore, it is the greatest common factor, being the largest number that can divide both square roots without leaving a remainder.

C (14) YOUR ANSWER

Although 14 is a factor of itself, it is not a factor of 7. Since the GCF must be a common factor of both numbers, 14 cannot be the answer as it does not divide 7 evenly.

D (49) YOUR ANSWER

The number 49 is much larger than both 14 and 7. While it is a factor of 196 (since 196 = 49 x 4), it is not a factor of 7. Therefore, it cannot be the GCF of the two square roots.

Conclusion

The greatest common factor of the square roots of 196 and 49 is 7, as it is the largest number that divides both resulting values evenly. The other options do not meet the criteria for being a common factor, emphasizing the importance of determining shared divisibility when identifying the GCF.

Using prime factorization, what is the greatest common factor of the square root of 196 and the square root of 49?

7

Related Questions

Related Quizzes

How familiar were you with this question?

Report an Issue

Rate this Practice Test