Question

Find Greatest Common Divisor of 4666620000 and 6666600000, using prime factorization.

Answer

The GCD of given numbers is 666660000.

Explanation

Step 1 : Find prime factorization of each number.

4666620000 = 6666600000 = 2 \cdot 2 \cdot 2 \cdot 2 \cdot 2 \cdot 3 \cdot 5 \cdot 5 \cdot 5 \cdot 5 \cdot 7 \cdot 41 \cdot 271 2 \cdot 2 \cdot 2 \cdot 2 \cdot 2 \cdot 2 \cdot 3 \cdot 5 \cdot 5 \cdot 5 \cdot 5 \cdot 5 \cdot 41 \cdot 271

(view steps on how to factor 4666620000 and 6666600000. )

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

4666620000 = 6666600000 = 2 \cdot 2 \cdot 2 \cdot 2 \cdot 2 \cdot 3 \cdot 5 \cdot 5 \cdot 5 \cdot 5 \cdot 7 \cdot 41 \cdot 271 2 \cdot 2 \cdot 2 \cdot 2 \cdot 2 \cdot 2 \cdot 3 \cdot 5 \cdot 5 \cdot 5 \cdot 5 \cdot 5 \cdot 41 \cdot 271

Step 3 : Multiply the boxed numbers together:

GC D = 2 \cdot 2 \cdot 2 \cdot 2 \cdot 2 \cdot 3 \cdot 5 \cdot 5 \cdot 5 \cdot 5 \cdot 41 \cdot 271 = 666660000

This solution can be visualized using a Venn diagram.

0,0

4666620000

6666600000

271

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

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