What is the greatest common factor of 27, 36, and 45?

The greatest common factor (GCF) of 27, 36, and 45 is 9.

To find the GCF, we first need to factor each number:

• 27 can be factored as 3 x 3 x 3 or 3³.
• 36 can be factored as 2 x 2 x 3 x 3 or 2² x 3².
• 45 can be factored as 3 x 3 x 5 or 3² x 5.

Next, we look for the common factors in each of the numbers:

• The number 3 is a common factor in all three.
• 27 has 3³, 36 has 3², and 45 has 3².

The lowest power of the common factor (which is 3) among these is 3², which equals 9.

Thus, the greatest common factor of 27, 36, and 45 is 9.