Question

Find Greatest Common Divisor of 216, 900, 36, 120, 144, 108, 49, 60, 150 and 25, using prime factorization.

Answer

The GCD of given numbers is 1.

Explanation

Step 1 : Find prime factorization of each number.

216 = 900 = 36 = 120 = 144 = 108 = 49 = 60 = 150 = 25 = 2 \cdot 2 \cdot 2 \cdot 3 \cdot 3 \cdot 3 2 \cdot 2 \cdot 3 \cdot 3 \cdot 5 \cdot 5 2 \cdot 2 \cdot 3 \cdot 3 2 \cdot 2 \cdot 2 \cdot 3 \cdot 5 2 \cdot 2 \cdot 2 \cdot 2 \cdot 3 \cdot 3 2 \cdot 2 \cdot 3 \cdot 3 \cdot 3 7 \cdot 7 2 \cdot 2 \cdot 3 \cdot 5 2 \cdot 3 \cdot 5 \cdot 5 5 \cdot 5

(view steps on how to factor 216, 900, 36, 120, 144, 108, 49, 60, 150 and 25. )

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

216 = 900 = 36 = 120 = 144 = 108 = 49 = 60 = 150 = 25 = 2 \cdot 2 \cdot 2 \cdot 3 \cdot 3 \cdot 3 2 \cdot 2 \cdot 3 \cdot 3 \cdot 5 \cdot 5 2 \cdot 2 \cdot 3 \cdot 3 2 \cdot 2 \cdot 2 \cdot 3 \cdot 5 2 \cdot 2 \cdot 2 \cdot 2 \cdot 3 \cdot 3 2 \cdot 2 \cdot 3 \cdot 3 \cdot 3 7 \cdot 7 2 \cdot 2 \cdot 3 \cdot 5 2 \cdot 3 \cdot 5 \cdot 5 5 \cdot 5

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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