Question

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

Answer 1

Answer: 8

Step-by-step 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