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# Issues on Discovering Unit Digit

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 7153 :

7 =  7 (Unit digit is 7)

72  =  49 (Unit digit is 9)

73  =  343 (Unit digit is 3)

7 =  2401 (Unit digit is 1)

7 =   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 seven153 is 7.

Unit digit of 251 is 1

Evaluating 172 :

Unit digit of 172 is 1.

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

Drawback 3 :

What’s the unit digit in 264102 + 264103 ?

Resolution :

=  264 102 + 264 103

=  264 102 (1 + 264)

=  264 102 (265)

Calculating the cyclicity of 4 :

41  =  4

42  =  16

43  =  64

44  =  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 seven95 – 358 ?

Resolution :

Cyclicity of seven :

71  =  7 (Unit digit is 7)

72  =  49 (Unit digit is 9)

73  =  343 (Unit digit is 3)

74  =  2401 (Unit digit is 1)

75  =  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 :

31  =  3 (Unit digit is 3)

32  =  9 (Unit digit is 9)

33  =  27 (Unit digit is 7)

34  =  81 (Unit digit is 1)

35  =  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 {63741793 x 625317 x 341491} ?

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 63741793 is 4, the unit digit of 625317 is 5 and the unit digit of 341491 is 1.

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

Therefore the unit digit is 0. Kindly mail your suggestions to v4formath@gmail.com

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