Question

waht is unit digit in 7 ^ 105

Answer 1

5 is unit digit

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Answer 2

First note that 7^1 = 7, 7^2=49, 7^3 =343 and 7^4 = 2401 and then the pattern in the unit’s place repeats. That is, 7, 9, 3, 1.

That means the units place for every 7^(1+4n) is 7 and for 7^(2+4n) is 9 and so on for an integer n.

Now consider 105 = 1 + 4 *26, which by above logic will have 7 in the units place.