Question

what is the greatest common factor of 27 and 36? the greatest common factor of 27 and 36 is .

Explanation:

Step1: Find factors of 27

The factors of 27 are all the numbers that divide 27 without leaving a remainder. So, \(1\times27 = 27\), \(3\times9 = 27\). Thus, the factors of 27 are \(1, 3, 9, 27\).

Step2: Find factors of 36

The factors of 36 are found by identifying numbers that multiply to 36. \(1\times36 = 36\), \(2\times18 = 36\), \(3\times12 = 36\), \(4\times9 = 36\), \(6\times6 = 36\). So, the factors of 36 are \(1, 2, 3, 4, 6, 9, 12, 18, 36\).

Step3: Identify common factors

Now, we find the common factors of 27 and 36 by looking at the intersection of the two sets of factors. The common factors are \(1, 3, 9\).

Step4: Determine the greatest common factor

Among the common factors \(1, 3, 9\), the greatest one is 9.

Answer:

9