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Hint: Find all the factors of both the elements and then choose the ones which are common for both.

Complete step-by-step answer:

Factors of 35 = 1,5,7,35

Let us assume factors of 35 is Set A {1,5,7,35}

Factors of 50 = 1, 2, 5, 10, 25, 50

Let us assume factors of 50 is Set B {1,2,5,10,25,50}

Common factors are the intersection of Set A and Set B.

$ \Rightarrow {\text{A}} \cap {\text{B}} = \left\{ {1,5} \right\} \\$

So, these are your common factors.

Note: In these types of questions first calculate the factors of each element, then make a set of the factors of each element. Then conduct the operation on the sets based on what is asked.