Find the prime factorization of number 216000.

Answer

The prime factorization of 216000 is:

$$ 216000 = 2\cdot2\cdot2\cdot2\cdot2\cdot2\cdot3\cdot3\cdot3\cdot5\cdot5\cdot5 $$

Which is the same as :

$$ 216000 = 2^{6}\cdot3^{3}\cdot5^{3} $$

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

216000 can be written as 10 × 21600.	216000 10 21600
10 can be written as 2 × 5.	216000 10 5 2 21600
21600 can be written as 10 × 2160.	216000 10 5 2 21600 10 2160
10 can be written as 2 × 5.	216000 10 5 2 21600 10 5 2 2160
2160 can be written as 10 × 216.	216000 10 5 2 21600 10 5 2 2160 10 216
10 can be written as 2 × 5.	216000 10 5 2 21600 10 5 2 2160 10 5 2 216
216 can be written as 2 × 108.	216000 10 5 2 21600 10 5 2 2160 10 5 2 216 2 108
108 can be written as 2 × 54.	216000 10 5 2 21600 10 5 2 2160 10 5 2 216 2 108 54 2
54 can be written as 2 × 27.	216000 10 5 2 21600 10 5 2 2160 10 5 2 216 2 108 54 2 27 2
27 can be written as 3 × 9.	216000 10 5 2 21600 10 5 2 2160 10 5 2 216 2 108 54 2 27 9 3 2
9 can be written as 3 × 3.	216000 10 5 2 21600 10 5 2 2160 10 5 2 216 2 108 54 2 27 9 3 3 3 2
The end nodes are the prime factors of the number 216000.	216000 10 5 2 21600 10 5 2 2160 10 5 2 216 2 108 54 2 27 9 3 3 3 2

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