Find the prime factorization of number 13824.

Answer

The prime factorization of 13824 is:

$$ 13824 = 2\cdot2\cdot2\cdot2\cdot2\cdot2\cdot2\cdot2\cdot2\cdot3\cdot3\cdot3 $$

Which is the same as :

$$ 13824 = 2^{9}\cdot3^{3} $$

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

13824 can be written as 2 × 6912.	13824 2 6912
6912 can be written as 2 × 3456.	13824 2 6912 3456 2
3456 can be written as 2 × 1728.	13824 2 6912 3456 2 1728 2
1728 can be written as 2 × 864.	13824 2 6912 3456 2 1728 864 2 2
864 can be written as 2 × 432.	13824 2 6912 3456 2 1728 864 2 432 2 2
432 can be written as 2 × 216.	13824 2 6912 3456 2 1728 864 2 432 216 2 2 2
216 can be written as 2 × 108.	13824 2 6912 3456 2 1728 864 2 432 216 2 108 2 2 2
108 can be written as 2 × 54.	13824 2 6912 3456 2 1728 864 2 432 216 2 108 54 2 2 2 2
54 can be written as 2 × 27.	13824 2 6912 3456 2 1728 864 2 432 216 2 108 54 2 27 2 2 2 2
27 can be written as 3 × 9.	13824 2 6912 3456 2 1728 864 2 432 216 2 108 54 2 27 9 3 2 2 2 2
9 can be written as 3 × 3.	13824 2 6912 3456 2 1728 864 2 432 216 2 108 54 2 27 9 3 3 3 2 2 2 2
The end nodes are the prime factors of the number 13824.	13824 2 6912 3456 2 1728 864 2 432 216 2 108 54 2 27 9 3 3 3 2 2 2 2

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