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Question

Find the prime factorization of number 6000000.

Answer

The prime factorization of 6000000 is:
$6000000 = 2 \cdot 2 \cdot 2 \cdot 2 \cdot 2 \cdot 2 \cdot 2 \cdot 3 \cdot 5 \cdot 5 \cdot 5 \cdot 5 \cdot 5 \cdot 5$
Which is the same as :
$6000000 = 2^{7} \cdot 3 \cdot 5^{6}$

Explanation

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

6000000 can be written as 10 × 600000.	6000000 10 600000
10 can be written as 2 × 5.	6000000 10 5 2 600000
600000 can be written as 10 × 60000.	6000000 10 5 2 600000 10 60000
10 can be written as 2 × 5.	6000000 10 5 2 600000 10 5 2 60000
60000 can be written as 10 × 6000.	6000000 10 5 2 600000 10 5 2 60000 10 6000
10 can be written as 2 × 5.	6000000 10 5 2 600000 10 5 2 60000 10 5 2 6000
6000 can be written as 10 × 600.	6000000 10 5 2 600000 10 5 2 60000 10 5 2 6000 10 600
10 can be written as 2 × 5.	6000000 10 5 2 600000 10 5 2 60000 10 5 2 6000 10 5 2 600
600 can be written as 10 × 60.	6000000 10 5 2 600000 10 5 2 60000 10 5 2 6000 10 5 2 600 10 60
10 can be written as 2 × 5.	6000000 10 5 2 600000 10 5 2 60000 10 5 2 6000 10 5 2 600 10 5 2 60
60 can be written as 10 × 6.	6000000 10 5 2 600000 10 5 2 60000 10 5 2 6000 10 5 2 600 10 5 2 60 10 6
10 can be written as 2 × 5.	6000000 10 5 2 600000 10 5 2 60000 10 5 2 6000 10 5 2 600 10 5 2 60 10 5 2 6
6 can be written as 2 × 3.	6000000 10 5 2 600000 10 5 2 60000 10 5 2 6000 10 5 2 600 10 5 2 60 10 5 2 6 2 3
The end nodes are the prime factors of the number 6000000.	6000000 10 5 2 600000 10 5 2 60000 10 5 2 6000 10 5 2 600 10 5 2 60 10 5 2 6 2 3

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