Find the prime factorization of number 11520.

Answer

The prime factorization of 11520 is:

$$ 11520 = 2\cdot2\cdot2\cdot2\cdot2\cdot2\cdot2\cdot2\cdot3\cdot3\cdot5 $$

Which is the same as :

$$ 11520 = 2^{8}\cdot3^{2}\cdot5 $$

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

11520 can be written as 10 × 1152.	11520 10 1152
10 can be written as 2 × 5.	11520 10 5 2 1152
1152 can be written as 2 × 576.	11520 10 5 2 1152 2 576
576 can be written as 2 × 288.	11520 10 5 2 1152 2 576 288 2
288 can be written as 2 × 144.	11520 10 5 2 1152 2 576 288 2 144 2
144 can be written as 2 × 72.	11520 10 5 2 1152 2 576 288 2 144 72 2 2
72 can be written as 2 × 36.	11520 10 5 2 1152 2 576 288 2 144 72 2 36 2 2
36 can be written as 2 × 18.	11520 10 5 2 1152 2 576 288 2 144 72 2 36 18 2 2 2
18 can be written as 2 × 9.	11520 10 5 2 1152 2 576 288 2 144 72 2 36 18 2 9 2 2 2
9 can be written as 3 × 3.	11520 10 5 2 1152 2 576 288 2 144 72 2 36 18 2 9 3 3 2 2 2
The end nodes are the prime factors of the number 11520.	11520 10 5 2 1152 2 576 288 2 144 72 2 36 18 2 9 3 3 2 2 2

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