Drawback 1 :

What’s the unit digit within the product of

(684 x 759 x 413 x 676) ?

Resolution :

Product of unit digits of the given complete numbers is

= (4 x 9 x 3 x 6)

= 36 x 18

Unit digit of the product = 8.

So, the unit digit of the product of given complete numbers is 8.

Drawback 2 :

What’s the unit digit within the product

(3547)^{153} x (251)^{72} ?

Resolution :

Unit digit of 3547 is 7

Evaluating 7^{153 }:

7^{1 } = 7 (Unit digit is 7)

7^{2} = 49 (Unit digit is 9)

7^{3} = 343 (Unit digit is 3)

7^{4 } = 2401 (Unit digit is 1)

7^{5 } = 2401 x 7 (Unit digit is 7)

Each cycle consists of interval 4. By dividing 153 by 4, we get 1 as the rest. So, the unit digit of seven^{153} is 7.

Unit digit of 251 is 1

Evaluating 1^{72 }:

Unit digit of 1^{72 }is 1.

So, the unit digit of the given product is 7.

Drawback 3 :

What’s the unit digit in 264^{102} + 264^{103} ?

Resolution :

= 264 ^{102} + 264 ^{103}

= 264 ^{102} (1 + 264)

= 264^{ 102} (265)

Calculating the cyclicity of 4 :

4^{1} = 4

4^{2} = 16

4^{3} = 64

4^{4} = 256

Each cycle consists of interval 2.By dividing 102 by 2, we’ll get 0 as the rest. So, the unit digit of 4^{ 102 }is 6.

6(5) = 30 (unit digit is 0)

So, the required unit digit is 0.

Drawback 4 :

What’s the unit digit of seven^{95} – 3^{58} ?

Resolution :

Cyclicity of seven :

7^{1 }= 7 (Unit digit is 7)

7^{2} = 49 (Unit digit is 9)

7^{3} = 343 (Unit digit is 3)

7^{4 }= 2401 (Unit digit is 1)

7^{5 }= 2401 x 7 (Unit digit is 7)

Each cycle consists of interval 4.

By dividing 95 by 4, we get 3 as the rest. In response to cyclicity of seven, 3 would be the unit digit.

Cyclicity of three :

3^{1 }= 3 (Unit digit is 3)

3^{2} = 9 (Unit digit is 9)

3^{3} = 27 (Unit digit is 7)

3^{4 }= 81 (Unit digit is 1)

3^{5 }= 243 (Unit digit is 3)

Each cycle consists of interval 4.

By dividing 58 by 4, we get 2 as the rest. In response to cyclicity of three, 9 would be the unit digit.

13 – 9 = 4.

Drawback 5 :

What’s the unit digit in {6374^{1793} x 625^{317} x 341^{491}} ?

Resolution :

Cyclicity of 4 consists of interval 2. By multiplying 5 and 1 itself, we’ll get the identical 5 and 1 as unit digits.

Unit digit of 6374^{1793 }is 4, the unit digit of 625^{317 }is 5 and the unit digit of 341^{491 }is 1.

Product of unit digits = 4 x 5 x 1 = 20

Therefore the unit digit is 0.

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