Question

Find Greatest Common Divisor of 16128, 27216 and 25200, using prime factorization.

Answer

The GCD of given numbers is 1008.

Explanation

Step 1 : Find prime factorization of each number.

16128 = 27216 = 25200 = 2 \cdot 2 \cdot 2 \cdot 2 \cdot 2 \cdot 2 \cdot 2 \cdot 2 \cdot 3 \cdot 3 \cdot 7 2 \cdot 2 \cdot 2 \cdot 2 \cdot 3 \cdot 3 \cdot 3 \cdot 3 \cdot 3 \cdot 7 2 \cdot 2 \cdot 2 \cdot 2 \cdot 3 \cdot 3 \cdot 5 \cdot 5 \cdot 7

(view steps on how to factor 16128, 27216 and 25200. )

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

16128 = 27216 = 25200 = 2 \cdot 2 \cdot 2 \cdot 2 \cdot 2 \cdot 2 \cdot 2 \cdot 2 \cdot 3 \cdot 3 \cdot 7 2 \cdot 2 \cdot 2 \cdot 2 \cdot 3 \cdot 3 \cdot 3 \cdot 3 \cdot 3 \cdot 7 2 \cdot 2 \cdot 2 \cdot 2 \cdot 3 \cdot 3 \cdot 5 \cdot 5 \cdot 7

Step 3 : Multiply the boxed numbers together:

GC D = 2 \cdot 2 \cdot 2 \cdot 2 \cdot 3 \cdot 3 \cdot 7 = 1008

This solution can be visualized using a Venn diagram.

0,0

16128

27216

25200

The GCD equals the product of the numbers at the intersection.

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