Question

find the greatest common factor of 27 and 36.

Explanation:

Step1: Prime factorize 27

To find the prime factors of 27, we start by dividing by the smallest prime number. We know that \(27\div3 = 9\), then \(9\div3=3\), and \(3\div3 = 1\). So the prime factorization of 27 is \(27=3\times3\times3\).

Step2: Prime factorize 36

For 36, we start with \(36\div2 = 18\), \(18\div2=9\), \(9\div3 = 3\), \(3\div3=1\). So the prime factorization of 36 is \(36 = 2\times2\times3\times3\).

Step3: Identify common prime factors

From the prime factorizations, the common prime factor between 27 and 36 is 3. Now we find the minimum exponent of 3 in both factorizations. In 27, the exponent of 3 is 3, and in 36, the exponent of 3 is 2. So we take \(3^2\).

Step4: Calculate the GCF

\(3^2=9\).

Answer:

9