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"Colored chips": Factoring 16000 quickly

Link

https://gre.magoosh.com/questions/297

 

Question

FAQ: Can you tell me what is fastest way to go from 16000 to (2 * 2 * 2 * 2 * 2 * 2 * 2 * 5 * 5 * 5)?

 

Answer

Probably the easiest way is to draw out factors of 10. When we multiply something by 10, we simply add a 0 to the end, and when we divide by 10, we remove a 0. So,

16000 =

1600 * 10 =

160 * 10 * 10 =

16 * 10 * 10 * 10

From there, you know that 10 = 5 * 2, and 16 = 2^4, so:

16 * 10 * 10 * 10 = (2 * 2 * 2 * 2)(5 * 2)(5 * 2)(5 * 2)

 

 

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