Find the prime factorization of number 8192.

Answer

The prime factorization of 8192 is:

$$ 8192 = 2\cdot2\cdot2\cdot2\cdot2\cdot2\cdot2\cdot2\cdot2\cdot2\cdot2\cdot2\cdot2 $$

Which is the same as :

$$ 8192 = 2^{13} $$

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

8192 can be written as 2 × 4096.	8192 2 4096
4096 can be written as 2 × 2048.	8192 2 4096 2048 2
2048 can be written as 2 × 1024.	8192 2 4096 2048 2 1024 2
1024 can be written as 2 × 512.	8192 2 4096 2048 2 1024 512 2 2
512 can be written as 2 × 256.	8192 2 4096 2048 2 1024 512 2 256 2 2
256 can be written as 2 × 128.	8192 2 4096 2048 2 1024 512 2 256 128 2 2 2
128 can be written as 2 × 64.	8192 2 4096 2048 2 1024 512 2 256 128 2 64 2 2 2
64 can be written as 2 × 32.	8192 2 4096 2048 2 1024 512 2 256 128 2 64 32 2 2 2 2
32 can be written as 2 × 16.	8192 2 4096 2048 2 1024 512 2 256 128 2 64 32 2 16 2 2 2 2
16 can be written as 2 × 8.	8192 2 4096 2048 2 1024 512 2 256 128 2 64 32 2 16 8 2 2 2 2 2
8 can be written as 2 × 4.	8192 2 4096 2048 2 1024 512 2 256 128 2 64 32 2 16 8 2 4 2 2 2 2 2
4 can be written as 2 × 2.	8192 2 4096 2048 2 1024 512 2 256 128 2 64 32 2 16 8 2 4 2 2 2 2 2 2 2
The end nodes are the prime factors of the number 8192.	8192 2 4096 2048 2 1024 512 2 256 128 2 64 32 2 16 8 2 4 2 2 2 2 2 2 2

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