Aptitude - Numbers - Discussion

How 26 comes? Explain.

I too tried the same method @Shadab.

Is the method right or wrong, if yes then why? please explain it.

What is the unit digit? How can we find?

Please explain with example.

Please explain simple and easy method.

Can we find it by using log?

Exp :
7^0 = 1 unit digit = 1.
7^1 = 7 unit digit = 7.
7^2 = 49 unit digit = 9.
7^3 = 343 unit digit = 3.
7^4 = 2401 unit digit = 1.
7^5 = 16807 unit digit = 7.
7^6 = 117649. unit digit = 9.

Look at the unit digit of each exponent then u gonna find the pattern repeats after 4 times (1,7,9,3,then 1,7,9,3 then 1,7,9,3).

Instead of counting until 105 we divide by 4 and the remainder is the new exponent for 7.
in this case 105/4 = 26 1/4 the remainder is 1 so 7^1=7.

If 7^106 106/4=26 2/4 the remainder is 2 then 7^2 = 49 the unit digit is 9 and for sure 7^107 unit digit going to be 3 and 7^108 is 1 and so on.

7^105.

Firstly, divide the given power number by 4 (105/4=remainder is 1), then remove the given power and add remainder 1 as power (7^1), now 7 to the power 1 is 7. So, the answer is "7".