7th Class Mathematics Exponents and Power

  • question_answer 5) Express each of the following as product of powers of their prime factors: (i) 648                                    (ii) 405                                   (iii) 540                                  (iv) 3600.

    Answer:

                    (i) 648

    2 648
    2 324
    2 162
    2 81
    2 27
    2 9
    2 3
    2 1
    \[\therefore \]  \[648=2\times 2\times 2\times 3\times 3\times 3\times 3\]                 It is the required prime factor product form.                 (ii) 405
    3 405
    3 135
    3 45
    3 15
    5 5
    1
    \[\therefore \]  \[405=3\times 3\times 3\times 3\times 5\]                 \[={{3}^{4}}\times 5\]                 It is the required prime factor product form.                 (iii) 540
    2 540
    2 270
    3 135
    3 45
    3 15
    5 5
    1
    \[\therefore \]  \[540=2\times 2\times 3\times 3\times 3\times 5\]                 \[={{2}^{2}}\times {{3}^{3}}\times 5\]                 It is the required prime factor product form.                 (iv) 3600
    2 3600
    2 1800
    2 900
    2 450
    3 225
    3 75
    5 25
    5 5
    1
    \[\therefore \]  \[3600=2\times 2\times 2\times 2\times 3\times 3\times 5\times 5\]                 \[={{2}^{4}}\times {{3}^{2}}\times {{5}^{2}}\]                 It is the required prime factor product form.

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