catita5 catita5
  • 25-07-2020
  • Mathematics
contestada

El resultado de \(2^{40}+2^{39}+2^{36}\) es divisible por i) 8 ii) 10 iii) 100

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jimthompson5910 jimthompson5910
  • 25-07-2020

Answer:  8

Explanation:

We can factor out 8 like so

2^40 + 2^39 + 2^36 = 2^3*2^37 + 2^3*2^36 + 2^3*2^33

2^40 + 2^39 + 2^36 = 2^3*(2^37 + 2^36 + 2^33)

2^40 + 2^39 + 2^36 = 8*(2^37 + 2^36 + 2^33)

Showing that 8 is a factor of 2^40 + 2^39 + 2^36

In other words, 2^40 + 2^39 + 2^36 is divisible by 8

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