Question
Find the prime factorization of number 3628800.
Answer
The prime factorization of 3628800 is:
$$ 3628800 = 2\cdot2\cdot2\cdot2\cdot2\cdot2\cdot2\cdot2\cdot3\cdot3\cdot3\cdot3\cdot5\cdot5\cdot7 $$Which is the same as :
$$ 3628800 = 2^{8}\cdot3^{4}\cdot5^{2}\cdot7 $$Explanation
Prime factorization can be nicely visualized by creating a factorization tree.
| 3628800 can be written as 10 × 362880. |
|
| 10 can be written as 2 × 5. |
|
| 362880 can be written as 10 × 36288. |
|
| 10 can be written as 2 × 5. |
|
| 36288 can be written as 2 × 18144. |
|
| 18144 can be written as 2 × 9072. |
|
| 9072 can be written as 2 × 4536. |
|
| 4536 can be written as 2 × 2268. |
|
| 2268 can be written as 2 × 1134. |
|
| 1134 can be written as 2 × 567. |
|
| 567 can be written as 3 × 189. |
|
| 189 can be written as 3 × 63. |
|
| 63 can be written as 3 × 21. |
|
| 21 can be written as 3 × 7. |
|
| The end nodes are the prime factors of the number 3628800. |
|
This page was created using
Prime factorization calculator