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How many positive five-digit numbers are divisible by each of 7, 8, 9, 10, and 11?

 Jun 15, 2021
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5-digit numbers divisible by 7 = 10003, 10010, 10017,..., 99995

So this is an AP with a = 10003, d = 7, and an = 99995

⇒ 99995 = 10003 + (n-1)7

⇒(n-1)7 = 89992 

⇒ n = 12857

∴ 7 has 12857 5-digit factors.  

 

Similarly,

5-digit numbers divisible by 8 = 10000, 10008, 10016,..., 99992

a = 10000, d = 8 and a= 99992 

 

5-digit numbers divisible by 9 = 10008, 10017, 10026,..., 99999

a = 10008, d = 9 and a= 99999 

 

5-digit numbers divisible by 10 = 10000, 10010, 10020,..., 99990

a = 10000, d = 10 and a= 99990

 

5-digit numbers divisible by 11 = 10010, 10021, 10032,..., 99990

a = 10010, d = 11 and a= 99990

 

 

...Rest you know how to find the total no. through AP...

 

~Hope you got it.

 Jun 16, 2021

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