Question

Find the unit digit of (345)^2020 + (366)^2019-(364) 1990
options:
0
2
6
5
3​

Answer 1

Answer:

6

Step-by-step explanation:

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Answer 2

Answer:

5

Step-by-step explanation:

Concept= Divisibility

Given= Numeric Equation

To find= Unit place digit

Explanation=

To  find the unit place of (345)^2020 + (366)^2019-(364)^1990 we need to separately find the unit place of each number.

We proceed with (345)^2020

the unit place of 345 is 5.

we make the cyclic repetition of 5 as 5^1=5

                                                               5^2=25

                                                               5^3=125

     Here at each place the unit is 5. So we divide 2020 with 5 which is fully divisible so the unit place finally will be 5 of (345)^2020

For (366)^2019

Unit place of 366 is 6

Cyclic repetition of 6 will be 6,36,216 the unit place is 6 only. We divide 2019 with 6 the remainder is 3 and in cyclic the unit place in power 3 is 6.

So the unit place of (366)^2019 is 6.

Lastly for (364)^1990

unit place of 364= 4

cyclic repetition 4^1=4

                           4^2=16

                           4^3=64

                           4^4=256

we divide 1990 with 4 we get remainder 2. So the cyclic value of power 2  at unit place is 6.

the unit place value of (364)^1990 is 6.

Equating in (345)^2020 + (366)^2019-(364)^1990 we get

5+6-6=5

Therefore the unit place of  (345)^2020 + (366)^2019-(364)^1990 is 5.

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