Find the prime factorization of number 162000.

Answer

The prime factorization of 162000 is:

$$ 162000 = 2\cdot2\cdot2\cdot2\cdot3\cdot3\cdot3\cdot3\cdot5\cdot5\cdot5 $$

Which is the same as :

$$ 162000 = 2^{4}\cdot3^{4}\cdot5^{3} $$

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

162000 can be written as 10 × 16200.	162000 10 16200
10 can be written as 2 × 5.	162000 10 5 2 16200
16200 can be written as 10 × 1620.	162000 10 5 2 16200 10 1620
10 can be written as 2 × 5.	162000 10 5 2 16200 10 5 2 1620
1620 can be written as 10 × 162.	162000 10 5 2 16200 10 5 2 1620 10 162
10 can be written as 2 × 5.	162000 10 5 2 16200 10 5 2 1620 10 5 2 162
162 can be written as 2 × 81.	162000 10 5 2 16200 10 5 2 1620 10 5 2 162 2 81
81 can be written as 3 × 27.	162000 10 5 2 16200 10 5 2 1620 10 5 2 162 2 81 27 3
27 can be written as 3 × 9.	162000 10 5 2 16200 10 5 2 1620 10 5 2 162 2 81 27 3 9 3
9 can be written as 3 × 3.	162000 10 5 2 16200 10 5 2 1620 10 5 2 162 2 81 27 3 9 3 3 3
The end nodes are the prime factors of the number 162000.	162000 10 5 2 16200 10 5 2 1620 10 5 2 162 2 81 27 3 9 3 3 3

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