Question

Find Greatest Common Divisor of 218, 908, 36, 124, 144, 180, 49, 60, 150 and 4, using prime factorization.

Answer

The GCD of given numbers is 1.

Explanation

Step 1 : Find prime factorization of each number.

218 = 908 = 36 = 124 = 144 = 180 = 49 = 60 = 150 = 4 = 2 \cdot 109 2 \cdot 2 \cdot 227 2 \cdot 2 \cdot 3 \cdot 3 2 \cdot 2 \cdot 31 2 \cdot 2 \cdot 2 \cdot 2 \cdot 3 \cdot 3 2 \cdot 2 \cdot 3 \cdot 3 \cdot 5 7 \cdot 7 2 \cdot 2 \cdot 3 \cdot 5 2 \cdot 3 \cdot 5 \cdot 5 2 \cdot 2

(view steps on how to factor 218, 908, 36, 124, 144, 180, 49, 60, 150 and 4. )

Step 2 : Put a box around factors that are common for all numbers:

218 = 908 = 36 = 124 = 144 = 180 = 49 = 60 = 150 = 4 = 2 \cdot 109 2 \cdot 2 \cdot 227 2 \cdot 2 \cdot 3 \cdot 3 2 \cdot 2 \cdot 31 2 \cdot 2 \cdot 2 \cdot 2 \cdot 3 \cdot 3 2 \cdot 2 \cdot 3 \cdot 3 \cdot 5 7 \cdot 7 2 \cdot 2 \cdot 3 \cdot 5 2 \cdot 3 \cdot 5 \cdot 5 2 \cdot 2

Note that in this example numbers do not have any common factors.

Step 3 : Multiply the boxed numbers together:

Since there is no boxed numbers we conclude that $GCD = 1$ .

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