Find the prime factorization of number 223014400.

Answer

The prime factorization of 223014400 is:

$$ 223014400 = 2\cdot2\cdot2\cdot2\cdot2\cdot2\cdot2\cdot2\cdot2\cdot5\cdot5\cdot7\cdot19\cdot131 $$

Which is the same as :

$$ 223014400 = 2^{9}\cdot5^{2}\cdot7\cdot19\cdot131 $$

Explanation

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

223014400 can be written as 10 × 22301440.	223014400 10 22301440
10 can be written as 2 × 5.	223014400 10 5 2 22301440
22301440 can be written as 10 × 2230144.	223014400 10 5 2 22301440 10 2230144
10 can be written as 2 × 5.	223014400 10 5 2 22301440 10 5 2 2230144
2230144 can be written as 2 × 1115072.	223014400 10 5 2 22301440 10 5 2 2230144 2 1115072
1115072 can be written as 2 × 557536.	223014400 10 5 2 22301440 10 5 2 2230144 2 1115072 557536 2
557536 can be written as 2 × 278768.	223014400 10 5 2 22301440 10 5 2 2230144 2 1115072 557536 2 278768 2
278768 can be written as 2 × 139384.	223014400 10 5 2 22301440 10 5 2 2230144 2 1115072 557536 2 278768 139384 2 2
139384 can be written as 2 × 69692.	223014400 10 5 2 22301440 10 5 2 2230144 2 1115072 557536 2 278768 139384 2 69692 2 2
69692 can be written as 2 × 34846.	223014400 10 5 2 22301440 10 5 2 2230144 2 1115072 557536 2 278768 139384 2 69692 34846 2 2 2
34846 can be written as 2 × 17423.	223014400 10 5 2 22301440 10 5 2 2230144 2 1115072 557536 2 278768 139384 2 69692 34846 2 17423 2 2 2
17423 can be written as 7 × 2489.	223014400 10 5 2 22301440 10 5 2 2230144 2 1115072 557536 2 278768 139384 2 69692 34846 2 17423 2489 7 2 2 2
2489 can be written as 19 × 131.	223014400 10 5 2 22301440 10 5 2 2230144 2 1115072 557536 2 278768 139384 2 69692 34846 2 17423 2489 19 131 7 2 2 2
The end nodes are the prime factors of the number 223014400.	223014400 10 5 2 22301440 10 5 2 2230144 2 1115072 557536 2 278768 139384 2 69692 34846 2 17423 2489 19 131 7 2 2 2

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