Question

what is the greatest common factor of 44 and 17?

Explanation:

Step1: Factorize 44

The factors of 44 are found by dividing 44 by all positive integers less than or equal to 44. So, \(44 = 1\times44 = 2\times22 = 4\times11\). Thus, the factors of 44 are \(1, 2, 4, 11, 22, 44\).

Step2: Factorize 17

17 is a prime number, so its only factors are \(1\) and \(17\).

Step3: Find common factors

The common factor of 44 and 17 is the number that appears in both lists of factors. From the factors of 44 (\(1, 2, 4, 11, 22, 44\)) and the factors of 17 (\(1, 17\)), the only common factor is \(1\).

Answer:

\(1\)