What is the remainder of \( 3^{37} \) when divided by 10Theory: Remainder of a number by 10 is same as the unit's digit of the number(
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How to find Remainders of Numbers by 10)
Using Above theory Remainder of \( 3^{37} \) by 10 = unit's digit of \( 3^{37} \)
Now to find the unit's digit of \( 3^{37} \) , we need to find the pattern / cycle of unit's digit of power of 3 and then generalizing it.
Unit's digit of \(3^1\) = 3
Unit's digit of \(3^2\) = 9
Unit's digit of \(3^3\) = 7
Unit's digit of \(3^4\) = 1
Unit's digit of \(3^5\) = 3
So, unit's digit of power of 3 repeats after every \(4^{th}\) number.
=> We need to divided 37 by 4 and check what is the remainder
=> 37 divided by 4 gives 1 remainder
=> \( 3^{37} \) will have the same unit's digit as \(3^1\) = 3
So,
Answer will be BHope it helps!
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