Find the prime factorization of number 1440.

Answer

The prime factorization of 1440 is:
$1440 = 2 \cdot 2 \cdot 2 \cdot 2 \cdot 2 \cdot 3 \cdot 3 \cdot 5$
Which is the same as :
$1440 = 2^{5} \cdot 3^{2} \cdot 5$

Explanation

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

1440 can be written as 10 × 144.	1440 10 144
10 can be written as 2 × 5.	1440 10 5 2 144
144 can be written as 2 × 72.	1440 10 5 2 144 2 72
72 can be written as 2 × 36.	1440 10 5 2 144 2 72 36 2
36 can be written as 2 × 18.	1440 10 5 2 144 2 72 36 2 18 2
18 can be written as 2 × 9.	1440 10 5 2 144 2 72 36 2 18 9 2 2
9 can be written as 3 × 3.	1440 10 5 2 144 2 72 36 2 18 9 3 3 2 2
The end nodes are the prime factors of the number 1440.	1440 10 5 2 144 2 72 36 2 18 9 3 3 2 2

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Find the prime factorization of number 1440.

The prime factorization of 1440 is:1440=2⋅2⋅2⋅2⋅2⋅3⋅3⋅5 Which is the same as :1440=25⋅32⋅5

The prime factorization of 1440 is:
$1440 = 2 \cdot 2 \cdot 2 \cdot 2 \cdot 2 \cdot 3 \cdot 3 \cdot 5$
Which is the same as :
$1440 = 2^{5} \cdot 3^{2} \cdot 5$