Question

31. The number of all positive integers less than
2005 and prime to it is
Sol. 2007 = 1
The lea​

Answer 1

Given:  Number 2005

To find : The number of all positive integers less than  2005 which are prime to 2005

Solution:

2005 = 5 *   401

Only numbers having factor of 5 and 401 will not be co prime

all others will be prime

Starting from 2

2 to 2004  - total numbers = 2003

Factors of 5  

5 , 10 , 15 ..............................................................2000

5 ( 1 , 2  , 3 ..........................................................400)

400 numbers

Factors of 401

401 , 802  , 1203 , 1604 ,

4 numbers

=> 2003 - 400 - 4

= 1599

1599 numbers less than 2005 are co prime with 2005

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