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Euclid's Division Algorithm

Which of the ...

Question

Which of the following numbers will completely divide 2^61+2^62+2^63+2^64?

a) 100
b) 10
c) 27
d) 17

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Solution

given that :

(2⁶¹ + 2⁶² + 2⁶³ + 2⁶⁴)

= 2⁶¹ x (1 + 2 + 2² + 2³) = 2⁶¹ x 15

= 2⁶⁰ x (2 x 15)

= (2⁶⁰ x 30), which is divisible by 10.

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