Question

what is the greatest common factor (gcf) of 14 and 35? the gcf of 14 and 35 is .

Explanation:

Step1: Find factors of 14

The factors of 14 are the numbers that divide 14 without leaving a remainder. So, \(14\div1 = 14\), \(14\div2 = 7\), \(14\div7 = 2\), \(14\div14 = 1\). Thus, the factors of 14 are \(1, 2, 7, 14\).

Step2: Find factors of 35

The factors of 35 are the numbers that divide 35 without leaving a remainder. So, \(35\div1 = 35\), \(35\div5 = 7\), \(35\div7 = 5\), \(35\div35 = 1\). Thus, the factors of 35 are \(1, 5, 7, 35\).

Step3: Identify the greatest common factor

From the factors of 14 (\(1, 2, 7, 14\)) and factors of 35 (\(1, 5, 7, 35\)), the common factors are \(1\) and \(7\). The greatest among these common factors is \(7\).

Answer:

7