2^31 is divisible with 5 what is the remainder?
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Answer:
3
Step-by-step explanation:
When 2^x is divided by 5 then the remainder always be one of 2,4,3 & 1 in that order.
The digits of the remainder repeat after every 4 digits (2, 4, 3, 1, 2, 4, 3, 1...)
This property is called cyclicity.
To find out the remainder when 2^31 is divided by 5, we divide the power by the cyclicity of its base and obtain the remainder.
>> 31/4 (remainder = 3)
Now we use this remainder as the power and apply it to the same base.
>> 2^3 = 8
Now divide this by 5.
>> 8/5 (The remainder is (3))
Due to the nature of this method, 2^31 /5 will give us the same remainder when 2^3 is divided by 5.
Answer = 3
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