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Question

Find the prime factorization of number 500000000.

Answer

The prime factorization of 500000000 is:
$$ 500000000 = 2\cdot2\cdot2\cdot2\cdot2\cdot2\cdot2\cdot2\cdot5\cdot5\cdot5\cdot5\cdot5\cdot5\cdot5\cdot5\cdot5 $$
Which is the same as :
$$ 500000000 = 2^{8}\cdot5^{9} $$

Explanation

Prime factorization can be nicely visualized by creating a factorization tree.

500000000 can be written as 10 × 50000000.	500000000 10 50000000
10 can be written as 2 × 5.	500000000 10 5 2 50000000
50000000 can be written as 10 × 5000000.	500000000 10 5 2 50000000 10 5000000
10 can be written as 2 × 5.	500000000 10 5 2 50000000 10 5 2 5000000
5000000 can be written as 10 × 500000.	500000000 10 5 2 50000000 10 5 2 5000000 10 500000
10 can be written as 2 × 5.	500000000 10 5 2 50000000 10 5 2 5000000 10 5 2 500000
500000 can be written as 10 × 50000.	500000000 10 5 2 50000000 10 5 2 5000000 10 5 2 500000 10 50000
10 can be written as 2 × 5.	500000000 10 5 2 50000000 10 5 2 5000000 10 5 2 500000 10 5 2 50000
50000 can be written as 10 × 5000.	500000000 10 5 2 50000000 10 5 2 5000000 10 5 2 500000 10 5 2 50000 10 5000
10 can be written as 2 × 5.	500000000 10 5 2 50000000 10 5 2 5000000 10 5 2 500000 10 5 2 50000 10 5 2 5000
5000 can be written as 10 × 500.	500000000 10 5 2 50000000 10 5 2 5000000 10 5 2 500000 10 5 2 50000 10 5 2 5000 10 500
10 can be written as 2 × 5.	500000000 10 5 2 50000000 10 5 2 5000000 10 5 2 500000 10 5 2 50000 10 5 2 5000 10 5 2 500
500 can be written as 10 × 50.	500000000 10 5 2 50000000 10 5 2 5000000 10 5 2 500000 10 5 2 50000 10 5 2 5000 10 5 2 500 10 50
10 can be written as 2 × 5.	500000000 10 5 2 50000000 10 5 2 5000000 10 5 2 500000 10 5 2 50000 10 5 2 5000 10 5 2 500 10 5 2 50
50 can be written as 10 × 5.	500000000 10 5 2 50000000 10 5 2 5000000 10 5 2 500000 10 5 2 50000 10 5 2 5000 10 5 2 500 10 5 2 50 10 5
10 can be written as 2 × 5.	500000000 10 5 2 50000000 10 5 2 5000000 10 5 2 500000 10 5 2 50000 10 5 2 5000 10 5 2 500 10 5 2 50 10 5 2 5
The end nodes are the prime factors of the number 500000000.	500000000 10 5 2 50000000 10 5 2 5000000 10 5 2 500000 10 5 2 50000 10 5 2 5000 10 5 2 500 10 5 2 50 10 5 2 5

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