Find the prime factorization of number 49152.

Answer

The prime factorization of 49152 is:

$$ 49152 = 2\cdot2\cdot2\cdot2\cdot2\cdot2\cdot2\cdot2\cdot2\cdot2\cdot2\cdot2\cdot2\cdot2\cdot3 $$

Which is the same as :

$$ 49152 = 2^{14}\cdot3 $$

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

49152 can be written as 2 × 24576.	49152 2 24576
24576 can be written as 2 × 12288.	49152 2 24576 12288 2
12288 can be written as 2 × 6144.	49152 2 24576 12288 2 6144 2
6144 can be written as 2 × 3072.	49152 2 24576 12288 2 6144 3072 2 2
3072 can be written as 2 × 1536.	49152 2 24576 12288 2 6144 3072 2 1536 2 2
1536 can be written as 2 × 768.	49152 2 24576 12288 2 6144 3072 2 1536 768 2 2 2
768 can be written as 2 × 384.	49152 2 24576 12288 2 6144 3072 2 1536 768 2 384 2 2 2
384 can be written as 2 × 192.	49152 2 24576 12288 2 6144 3072 2 1536 768 2 384 192 2 2 2 2
192 can be written as 2 × 96.	49152 2 24576 12288 2 6144 3072 2 1536 768 2 384 192 2 96 2 2 2 2
96 can be written as 2 × 48.	49152 2 24576 12288 2 6144 3072 2 1536 768 2 384 192 2 96 48 2 2 2 2 2
48 can be written as 2 × 24.	49152 2 24576 12288 2 6144 3072 2 1536 768 2 384 192 2 96 48 2 24 2 2 2 2 2
24 can be written as 2 × 12.	49152 2 24576 12288 2 6144 3072 2 1536 768 2 384 192 2 96 48 2 24 12 2 2 2 2 2 2
12 can be written as 2 × 6.	49152 2 24576 12288 2 6144 3072 2 1536 768 2 384 192 2 96 48 2 24 12 2 6 2 2 2 2 2 2
6 can be written as 2 × 3.	49152 2 24576 12288 2 6144 3072 2 1536 768 2 384 192 2 96 48 2 24 12 2 6 3 2 2 2 2 2 2 2
The end nodes are the prime factors of the number 49152.	49152 2 24576 12288 2 6144 3072 2 1536 768 2 384 192 2 96 48 2 24 12 2 6 3 2 2 2 2 2 2 2

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