What is the GCF of 27 and 36?

To find the greatest common factor (GCF) of 27 and 36, we can use different methods such as listing out the factors of each number, or using prime factorization. Here are the two methods:

Method 1: Listing out the factors

• The factors of 27 are 1, 3, 9, and 27
• The factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18, and 36
• The common factors of 27 and 36 are 1, 3, and 9
• The greatest common factor (GCF) of 27 and 36 is 9

Method 2: Prime factorization

• Prime factorization of 27: 3 x 3 x 3
• Prime factorization of 36: 2 x 2 x 3 x 3
• The common prime factors of 27 and 36 are 3 and 3
• The greatest common factor (GCF) of 27 and 36 is 3 x 3 = 9

Both methods yield the same result. Therefore, the GCF of 27 and 36 is 9.