Find the prime factorization of number 176400.

Answer

The prime factorization of 176400 is:

$$ 176400 = 2\cdot2\cdot2\cdot2\cdot3\cdot3\cdot5\cdot5\cdot7\cdot7 $$

Which is the same as :

$$ 176400 = 2^{4}\cdot3^{2}\cdot5^{2}\cdot7^{2} $$

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

176400 can be written as 10 × 17640.	176400 10 17640
10 can be written as 2 × 5.	176400 10 5 2 17640
17640 can be written as 10 × 1764.	176400 10 5 2 17640 10 1764
10 can be written as 2 × 5.	176400 10 5 2 17640 10 5 2 1764
1764 can be written as 2 × 882.	176400 10 5 2 17640 10 5 2 1764 2 882
882 can be written as 2 × 441.	176400 10 5 2 17640 10 5 2 1764 2 882 441 2
441 can be written as 3 × 147.	176400 10 5 2 17640 10 5 2 1764 2 882 441 3 147 2
147 can be written as 3 × 49.	176400 10 5 2 17640 10 5 2 1764 2 882 441 3 147 49 3 2
49 can be written as 7 × 7.	176400 10 5 2 17640 10 5 2 1764 2 882 441 3 147 49 7 7 3 2
The end nodes are the prime factors of the number 176400.	176400 10 5 2 17640 10 5 2 1764 2 882 441 3 147 49 7 7 3 2

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