Find the prime factorization of number 648000.

Answer

The prime factorization of 648000 is:

$$ 648000 = 2\cdot2\cdot2\cdot2\cdot2\cdot2\cdot3\cdot3\cdot3\cdot3\cdot5\cdot5\cdot5 $$

Which is the same as :

$$ 648000 = 2^{6}\cdot3^{4}\cdot5^{3} $$

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

648000 can be written as 10 × 64800.	648000 10 64800
10 can be written as 2 × 5.	648000 10 5 2 64800
64800 can be written as 10 × 6480.	648000 10 5 2 64800 10 6480
10 can be written as 2 × 5.	648000 10 5 2 64800 10 5 2 6480
6480 can be written as 10 × 648.	648000 10 5 2 64800 10 5 2 6480 10 648
10 can be written as 2 × 5.	648000 10 5 2 64800 10 5 2 6480 10 5 2 648
648 can be written as 2 × 324.	648000 10 5 2 64800 10 5 2 6480 10 5 2 648 2 324
324 can be written as 2 × 162.	648000 10 5 2 64800 10 5 2 6480 10 5 2 648 2 324 162 2
162 can be written as 2 × 81.	648000 10 5 2 64800 10 5 2 6480 10 5 2 648 2 324 162 2 81 2
81 can be written as 3 × 27.	648000 10 5 2 64800 10 5 2 6480 10 5 2 648 2 324 162 2 81 27 3 2
27 can be written as 3 × 9.	648000 10 5 2 64800 10 5 2 6480 10 5 2 648 2 324 162 2 81 27 3 9 3 2
9 can be written as 3 × 3.	648000 10 5 2 64800 10 5 2 6480 10 5 2 648 2 324 162 2 81 27 3 9 3 3 3 2
The end nodes are the prime factors of the number 648000.	648000 10 5 2 64800 10 5 2 6480 10 5 2 648 2 324 162 2 81 27 3 9 3 3 3 2

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