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Question

Find the prime factorization of number 100000000.

Answer

The prime factorization of 100000000 is:
$$ 100000000 = 2\cdot2\cdot2\cdot2\cdot2\cdot2\cdot2\cdot2\cdot5\cdot5\cdot5\cdot5\cdot5\cdot5\cdot5\cdot5 $$
Which is the same as :
$$ 100000000 = 2^{8}\cdot5^{8} $$

Explanation

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

100000000 can be written as 10 × 10000000.	100000000 10 10000000
10 can be written as 2 × 5.	100000000 10 5 2 10000000
10000000 can be written as 10 × 1000000.	100000000 10 5 2 10000000 10 1000000
10 can be written as 2 × 5.	100000000 10 5 2 10000000 10 5 2 1000000
1000000 can be written as 10 × 100000.	100000000 10 5 2 10000000 10 5 2 1000000 10 100000
10 can be written as 2 × 5.	100000000 10 5 2 10000000 10 5 2 1000000 10 5 2 100000
100000 can be written as 10 × 10000.	100000000 10 5 2 10000000 10 5 2 1000000 10 5 2 100000 10 10000
10 can be written as 2 × 5.	100000000 10 5 2 10000000 10 5 2 1000000 10 5 2 100000 10 5 2 10000
10000 can be written as 10 × 1000.	100000000 10 5 2 10000000 10 5 2 1000000 10 5 2 100000 10 5 2 10000 10 1000
10 can be written as 2 × 5.	100000000 10 5 2 10000000 10 5 2 1000000 10 5 2 100000 10 5 2 10000 10 5 2 1000
1000 can be written as 10 × 100.	100000000 10 5 2 10000000 10 5 2 1000000 10 5 2 100000 10 5 2 10000 10 5 2 1000 10 100
10 can be written as 2 × 5.	100000000 10 5 2 10000000 10 5 2 1000000 10 5 2 100000 10 5 2 10000 10 5 2 1000 10 5 2 100
100 can be written as 10 × 10.	100000000 10 5 2 10000000 10 5 2 1000000 10 5 2 100000 10 5 2 10000 10 5 2 1000 10 5 2 100 10 10
10 can be written as 2 × 5.	100000000 10 5 2 10000000 10 5 2 1000000 10 5 2 100000 10 5 2 10000 10 5 2 1000 10 5 2 100 10 5 2 10
10 can be written as 2 × 5.	100000000 10 5 2 10000000 10 5 2 1000000 10 5 2 100000 10 5 2 10000 10 5 2 1000 10 5 2 100 10 5 2 10 2 5
The end nodes are the prime factors of the number 100000000.	100000000 10 5 2 10000000 10 5 2 1000000 10 5 2 100000 10 5 2 10000 10 5 2 1000 10 5 2 100 10 5 2 10 2 5

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