Find Greatest Common Divisor of 6, 11, 17, 22, 28, 33, 38, 44, 49 and 55, using prime factorization.

Answer

The GCD of given numbers is 1.

Explanation

Step 1 : Find prime factorization of each number.

6 = 11 = 17 = 22 = 28 = 33 = 38 = 44 = 49 = 55 = 2 \cdot 3 1117 2 \cdot 11 2 \cdot 2 \cdot 7 3 \cdot 11 2 \cdot 19 2 \cdot 2 \cdot 11 7 \cdot 7 5 \cdot 11

(view steps on how to factor 6, 11, 17, 22, 28, 33, 38, 44, 49 and 55. )

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

6 = 11 = 17 = 22 = 28 = 33 = 38 = 44 = 49 = 55 = 2 \cdot 3 1117 2 \cdot 11 2 \cdot 2 \cdot 7 3 \cdot 11 2 \cdot 19 2 \cdot 2 \cdot 11 7 \cdot 7 5 \cdot 11

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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