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10 Oct 2005, 21:16
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What is the reminder of 7^381 divided by 5
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10 Oct 2005, 21:25
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The remainder is 2. We only need to know the last digit of 7^381 to know the remainder.
last digits are
7^0=1
7^1=7
7^2=9
7^3=3
7^4=1
7^5=7
as you may notice, the last digits repeat every 4 powers, ie., last digit of 7^2 = last digit of 7^6, etc.
381 is one more than 380 (which is divisible by 4), thus 7^381 will have the last digit 7, therefore the remainder will be 2
last digits are
7^0=1
7^1=7
7^2=9
7^3=3
7^4=1
7^5=7
as you may notice, the last digits repeat every 4 powers, ie., last digit of 7^2 = last digit of 7^6, etc.
381 is one more than 380 (which is divisible by 4), thus 7^381 will have the last digit 7, therefore the remainder will be 2
)
