Problem Solving

what is unit's digits of 2467^163 * 341^72??????

Units Digit :

Lets take the first part of the problem :

i.e. 2467^163..

Unit place of 2467 is 7, thus for powers of 7 the units place can be the following :

7
9
3
1
and then the cycle repeats..

Hence the power of 7 pertains to a 4 number cycle, divide the required power 163 by 4

163/4 leaves a reminder 3 hence from the cycle above the unit digit is 3.

Now the second part..

341^72

The unit digit of any power of 1 is again 1..

Thus 341^72 unit digit is 1.

Now multiply both the unit digits (3*1) = 3.

Thus the unit digit of the expression 2467^163 * 341^72 is 3.