Find Greatest Common Divisor of 576, 1152, 1280, 136 and 200, using prime factorization.

Answer

The GCD of given numbers is 8.

Explanation

Step 1 : Find prime factorization of each number.

576 = 1152 = 1280 = 136 = 200 = 2 \cdot 2 \cdot 2 \cdot 2 \cdot 2 \cdot 2 \cdot 3 \cdot 3 2 \cdot 2 \cdot 2 \cdot 2 \cdot 2 \cdot 2 \cdot 2 \cdot 3 \cdot 3 2 \cdot 2 \cdot 2 \cdot 2 \cdot 2 \cdot 2 \cdot 2 \cdot 2 \cdot 5 2 \cdot 2 \cdot 2 \cdot 17 2 \cdot 2 \cdot 2 \cdot 5 \cdot 5

(view steps on how to factor 576, 1152, 1280, 136 and 200. )

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

576 = 1152 = 1280 = 136 = 200 = 2 \cdot 2 \cdot 2 \cdot 2 \cdot 2 \cdot 2 \cdot 3 \cdot 3 2 \cdot 2 \cdot 2 \cdot 2 \cdot 2 \cdot 2 \cdot 2 \cdot 3 \cdot 3 2 \cdot 2 \cdot 2 \cdot 2 \cdot 2 \cdot 2 \cdot 2 \cdot 2 \cdot 5 2 \cdot 2 \cdot 2 \cdot 17 2 \cdot 2 \cdot 2 \cdot 5 \cdot 5

Step 3 : Multiply the boxed numbers together:

GC D = 2 \cdot 2 \cdot 2 = 8

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