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  • Playing With Numbers (RD Sharma –Chapter 2-Solution of Exercise 2.4)

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      RD Sharma - Exercise 2.4 - Solutions Page

      Playing With Numbers

      Exercise 2.4 (Prime Factorization)

       

      Question 1 (Refer Book - Mathematics Class VI R.D. Sharma)

      Solution:

      Prime Factorization is the process of expressing a given number as a product of prime factors.

      i. 24 = 2x3x4

      ii.56 = 1x7x2x2x2

      iii.70 = 2x5x7 (Here, Prime Factorization has been done)

      iv.54 = 2x3x9

      Question 2 (Refer Book - Mathematics Class VI R.D. Sharma)

      Solution:

      i. 216

        

      2

      216

      2

      108

      2

      54

      3

      27

      3

      9

       

      3

      Prime Factorization = 2x2x2x3x3x3

       

      ii. 420

       

      2

      420

      2

      210

      3

      105

      5

      35

       

      7

      Prime Factorization = 2x2x3x5x7

       

      iii. 468

       

      2

      468

      2

      234

      3

      117

      3

      39

       

      13

      Prime Factorization = 2x2x3x3x13

       

      iv. 945

       

      3

      945

      3

      315

      3

      105

      5

      35

       

      7

      Prime Factorization = 3x3x3x5x7

       

      v. 7325

       

      5

      7325

      5

      1465

       

      293

      Prime Factorization = 5x5x293

       

      vi. 13915

       

      5

      13915

      11

      2783

      11

      253

       

      23

      Question 3 (Refer Book - Mathematics Class VI R.D. Sharma)

      Solution:

      Smallest 4-digit number = 1000

      2

      1000

      2

      500

      2

      250

      5

      125

      5

      25

       

      5

      Prime Factorization = 2x2x2x5x5x5

      Question 4 (Refer Book - Mathematics Class VI R.D. Sharma)

      Solution:

      Largest 4-digit number = 9999

      3

      9999

      3

      3333

      11

      1111

       

      101

      Prime Factorization = 3x3x11x101

       

      Question 5 (Refer Book - Mathematics Class VI R.D. Sharma)

      Solution:

       

      7

      1729

      13

      247

       

      19

       

       

      Prime Factorization = 7x13x19

      Each factor is more than the previous factor.

      Question 6 (Refer Book - Mathematics Class VI R.D. Sharma)

      Solution:

      One and the number itself are not included in the prime factorization of a composite number.

       

      Question 7 (Refer Book - Mathematics Class VI R.D. Sharma)

      Solution:

      i.

       



      ii.