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Express each of the following numbers as a product of its prime factors:
(a) 7560
(b) 5005
Given :
The given numbers are 7560 and 5005.
To do :
We have to express the given numbers as a product of its prime factors.
Solution :
a) 7560
2 | 7560
__|________
2 | 3780
__|________
2 | 1890
__|________
3 | 945
__|________
3 | 315
__|________
3 | 105
__|________
5 | 35
__|________
7
$7560 = 2 \times 2 \times 2 \times 3 \times 3 \times 3\times 5 \times 7$
$= 2^3 \times 3^3 \times 5 \times 7$
Therefore, 7560 as a product of it's prime factors is $2^3 \times 3^3 \times 5 \times 7$.
b) 5005
5 | 5005
__|________
7 | 1001
__|________
11 | 143
__|________
| 13
$5005 = 5 \times 7 \times 11 \times 13$
Therefore, 5005 as a product of it's prime factors is $5 \times 7 \times 11 \times 13$