Question

find the greatest common factor (gcf). 9 and 36

Explanation:

Step1: List factors of 9

The factors of 9 are all the numbers that divide 9 without leaving a remainder. So, \(1, 3, 9\) (since \(9\div1 = 9\), \(9\div3 = 3\), \(9\div9 = 1\)).

Step2: List factors of 36

The factors of 36 are \(1, 2, 3, 4, 6, 9, 12, 18, 36\) (because \(36\div1 = 36\), \(36\div2 = 18\), \(36\div3 = 12\), \(36\div4 = 9\), \(36\div6 = 6\), \(36\div9 = 4\), \(36\div12 = 3\), \(36\div18 = 2\), \(36\div36 = 1\)).

Step3: Identify common factors

From the two lists, the common factors of 9 and 36 are \(1, 3, 9\).

Step4: Find the greatest common factor

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

Answer:

The greatest common factor of 9 and 36 is 9.