Find the prime factorization of number 3000.

Answer

The prime factorization of 3000 is:
$3000 = 2 \cdot 2 \cdot 2 \cdot 3 \cdot 5 \cdot 5 \cdot 5$
Which is the same as :
$3000 = 2^{3} \cdot 3 \cdot 5^{3}$

Explanation

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

3000 can be written as 10 × 300.	3000 10 300
10 can be written as 2 × 5.	3000 10 5 2 300
300 can be written as 10 × 30.	3000 10 5 2 300 10 30
10 can be written as 2 × 5.	3000 10 5 2 300 10 5 2 30
30 can be written as 10 × 3.	3000 10 5 2 300 10 5 2 30 10 3
10 can be written as 2 × 5.	3000 10 5 2 300 10 5 2 30 10 5 2 3
The end nodes are the prime factors of the number 3000.	3000 10 5 2 300 10 5 2 30 10 5 2 3

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Find the prime factorization of number 3000.

The prime factorization of 3000 is:3000=2⋅2⋅2⋅3⋅5⋅5⋅5 Which is the same as :3000=23⋅3⋅53

The prime factorization of 3000 is:
$3000 = 2 \cdot 2 \cdot 2 \cdot 3 \cdot 5 \cdot 5 \cdot 5$
Which is the same as :
$3000 = 2^{3} \cdot 3 \cdot 5^{3}$