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Question

Find the prime factorization of number 83531250.

Answer

The prime factorization of 83531250 is:
$83531250 = 2 \cdot 3 \cdot 3 \cdot 3 \cdot 3 \cdot 3 \cdot 5 \cdot 5 \cdot 5 \cdot 5 \cdot 5 \cdot 5 \cdot 11$
Which is the same as :
$83531250 = 2 \cdot 3^{5} \cdot 5^{6} \cdot 11$

Explanation

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

83531250 can be written as 10 × 8353125.	83531250 10 8353125
10 can be written as 2 × 5.	83531250 10 5 2 8353125
8353125 can be written as 5 × 1670625.	83531250 10 5 2 8353125 5 1670625
1670625 can be written as 5 × 334125.	83531250 10 5 2 8353125 5 1670625 334125 5
334125 can be written as 5 × 66825.	83531250 10 5 2 8353125 5 1670625 334125 5 66825 5
66825 can be written as 5 × 13365.	83531250 10 5 2 8353125 5 1670625 334125 5 66825 13365 5 5
13365 can be written as 5 × 2673.	83531250 10 5 2 8353125 5 1670625 334125 5 66825 13365 5 2673 5 5
2673 can be written as 3 × 891.	83531250 10 5 2 8353125 5 1670625 334125 5 66825 13365 5 2673 891 3 5 5
891 can be written as 3 × 297.	83531250 10 5 2 8353125 5 1670625 334125 5 66825 13365 5 2673 891 3 297 3 5 5
297 can be written as 3 × 99.	83531250 10 5 2 8353125 5 1670625 334125 5 66825 13365 5 2673 891 3 297 99 3 3 5 5
99 can be written as 3 × 33.	83531250 10 5 2 8353125 5 1670625 334125 5 66825 13365 5 2673 891 3 297 99 3 33 3 3 5 5
33 can be written as 3 × 11.	83531250 10 5 2 8353125 5 1670625 334125 5 66825 13365 5 2673 891 3 297 99 3 33 11 3 3 3 5 5
The end nodes are the prime factors of the number 83531250.	83531250 10 5 2 8353125 5 1670625 334125 5 66825 13365 5 2673 891 3 297 99 3 33 11 3 3 3 5 5

This page was created using

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