# PROBLEMS ON FINDING UNIT DIGIT OF THE PRODUCT OF WHOLE NUMBERS

Problem 1 :

What is the unit digit in the product of

(684 x 759 x 413 x 676) ?

Solution :

Product of unit digits of the given whole 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 whole numbers is 8.

Problem 2 :

What is the unit digit in the product

(3547)153 x (251)72 ?

Solution :

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)

Every cycle consists of interval 4. By dividing 153 by 4, we get 1 as remainder. So, the unit digit of 7153 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.

Problem 3 :

What is the unit digit in 264102 + 264103 ?

Solution :

=  264 102 + 264 103

=  264 102 (1 + 264)

=  264 102 (265)

Calculating the cyclicity of 4 :

41  =  4

42  =  16

43  =  64

44  =  256

Every cycle consists of interval 2.By dividing 102 by 2, we will get 0 as remainder. So, the unit digit of 4 102 is 6.

6(5)  =  30 (unit digit is 0)

So, the required unit digit is 0.

Problem 4 :

What is the unit digit of 795 - 358 ?

Solution :

Cyclicity of 7 :

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)

Every cycle consists of interval 4.

By dividing 95 by 4, we get 3 as remainder. According to cyclicity of 7, 3 will be the unit digit.

Cyclicity of 3 :

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)

Every cycle consists of interval 4.

By dividing 58 by 4, we get 2 as remainder. According to cyclicity of 3, 9 will be the unit digit.

13 - 9  =  4.

Problem 5 :

What is the unit digit in {63741793 x 625317 x 341491} ?

Solution :

Cyclicity of 4 consists of interval 2. By multiplying 5 and 1 itself, we will get the same 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

Hence the unit digit is 0.

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