Math, asked by nichurocks, 1 year ago

How many positive integers less than 1000 have the property that the sum of the digits of each such number is divisible by 7 and the number itself is divisible by 3

Answers

Answered by sajin2
6
Lets denote sum of the digits if a positive integer as 

For a number to be divisible by 3, the  should be divisible by 3

Also, we want integers whose  is divisible by 7

Therefore we want positive integers whose  is divisible by 21

Now maximum  for a 1-digit and 2-digit number is 9 and 18 respectively.

And since we want integers less than 1000, we want to find integers such as , i.e., 3-digit numbers only

The pair of 3 digits which has sum of 21 are 

1 of the above 8 pair has 3 same digits and the number of such integers can be given as 

3 of the above 8 pairs has 2 same digits and the number of such integers can be given as 

4 of the above 8 pairs has no common digits and the number of such integers can be given as 

 Positive integers with  divisible by 3 and 7 

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