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The number 345,600 can be expressed as 2^a*3^b*5^b for integers a, b and c. What is the value of the product abc?

 

\(\phantom{6^a5^b4^c}\) 

 Jul 9, 2022
 #1
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345,600  =

 

3456 x 100  =

 

576 x 6 x 100 =

 

24^2 x 2 x 3 x 10^2 =

 

6^2 x 4^2 x 2 x 3 x 2^2 x 5^2  =

 

2^2 x 3^2 x 2^4  x 2 x 3 x 2^2 x 5^2=

 

2^9 * 3^3 * 5^2

 

abc  = 9 * 3 * 2  =   54

 

cool cool cool

 Jul 9, 2022

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