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.