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Find the number of four-digit numbers which are not divisible by 4 or 5.

 May 6, 2022
 #1
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1- There are 1,800 multiples of 5 between 1,000 and 9,999

 

2- There are 2,250 multiples of 4 between 1,000 and 9,999

 

3- The LCM of (4, 5) ==20

 

4- There are 450 multiples of 20 between 1,000 and 9,999, which are already included in in (1) and (2) above that must be subtracted from their total.

 

5- There are 9,000 4-digit integers between 1,000 and 9,999.

 

6 - 1,800 + 2,250 - 450 ==3,600 multiple of 4 and 5

 

7 - 9,000 - 3,600 ==5,400 - 4-digit integers that are NOT divisible by 4 or by 5.

 May 6, 2022

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