# What is unit digit and how to find the unit digit of 7 to the power 105? (7^105)

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What is unit digit and how to find the unit digit of 7 to the power 105? (7^105)

Please say easy method and please explain correctly, because no one in web explained correctly.

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Ben Evansposted 3 years ago

If we look at this as geometric series it would look like:
7, 49, 343, 2401, 16807, 117,649.....................

The units digit is the digit on the right of the number.  The units digit is repeating like this:  7,9,3,1,7,9.  Each time we multiply by 7 the units digit will change and will follow the aforementioned sequence.

Because there are 4 numbers in the sequence, we take 105 and divide it by 4 and we get 26 with a remainder of 1.  If we go 4 times, the forth in the sequence is one, the eighth is 1, and the 12th is one.  7^104 will have a units digit of 1.   Because we have a remainder of 1, we count up 1 and that gives a units digit of 7.

The answer is the units digit of 7^105 is 7

working