Question

find the greatest common factor of 12 and 34.

Explanation:

Step1: Find factors of 12

The factors of 12 are the numbers that divide 12 without leaving a remainder. So, \(12 \div 1 = 12\), \(12 \div 2 = 6\), \(12 \div 3 = 4\), \(12 \div 4 = 3\), \(12 \div 6 = 2\), \(12 \div 12 = 1\). Thus, the factors of 12 are \(1, 2, 3, 4, 6, 12\).

Step2: Find factors of 34

The factors of 34 are the numbers that divide 34 without leaving a remainder. So, \(34 \div 1 = 34\), \(34 \div 2 = 17\), \(34 \div 17 = 2\), \(34 \div 34 = 1\). Thus, the factors of 34 are \(1, 2, 17, 34\).

Step3: Identify common factors

Now, we find the common factors of 12 and 34 by looking at the intersection of their factor sets. The common factors are \(1, 2\).

Step4: Determine the greatest common factor

Among the common factors \(1\) and \(2\), the greatest one is \(2\).

Answer:

2