Question

What is the GCF of 15 and 27? Provide a reason or explanation for your answer.

a) 3, because it is the smallest common factor.
b) 5, because it evenly divides both numbers.
c) 9, because it is the largest common factor.
d) 2, because it is the only even factor.

Answer 1

The GCF of 15 and 27 is 3, as it is the largest number that evenly divides both numbers and is the only common factor they share.

Step-by-step explanation:

The Greatest Common Factor (GCF) of 15 and 27 is determined by finding the largest number that evenly divides into both 15 and 27. Breaking down each number into prime factors, we find that 15 is the product of 3 times 5, while 27 is the product of 3 times 3 times 3. The only common factor between these two sets of prime factors is 3. Therefore, the correct answer is:

a) 3, because it is the smallest common factor.

This answer is not only correct because 3 is a common factor of both numbers, but also because it is the largest number that divides both 15 and 27 without leaving a remainder. The other options are incorrect because 5 does not divide into 27, 9 is not a factor of 15, and 2 is neither a factor of 15 nor 27 as both numbers are odd.