Question

What is the greatest common factor of 34 and 56?

Answer 1

Hint: In the given question, we are given two numbers of which we need to find the greatest common factor. In order to find the greatest common factor, we firstly need to find all the prime factors of 34 and 56 and then find out the common factors and multiply them in order to get the greatest common factor.

Complete step by step solution:
According to the given question, we need to find the greatest common factor of 34 and 56 and for that initially we need to find all the prime factors of these numbers and then we need to find the common factors in both and then multiplying them will give us the correct answer.
We need to remember that the multiplicity is also to be considered, that means, we need to take the repeated numbers also in order to find the greatest common factor.
Now, prime factors of 36 and 54 are:
$\begin{align}
  & 36=2\times 2\times 3\times 3 \\
 & 54=2\times 3\times 3\times 3 \\
\end{align}$
Now, clearly, we can see that 2, 3, 3 are the common factors of 36 and 54.
Therefore, the greatest common factor of 36 and 54 is 18.

Note: The greatest common factor is also called the highest common factor or greatest common divisor. There is another way like the long division method to find this but if we see in depth obviously the concepts or logic behind them are the same and we will of course get the same answer. It is just the procedure that is different.