Answer to Question #89541 in Algebra for Aravind

Question

Find the greatest number of four digits when divided by 3,5,7,9 leaves remainders 1,3,5,7 respectively

Answer 1

The greatest number of four digits is $9999.$

$$LCM(3,5,7,9)=5\times7\times9=315$$

Dividing $9999$ by $315$ we find that is largest four digit number that is evenly divisible by 3 , 5 , 7 and 9 is $9765.$

Common difference between divisors and respective remainders

$$3-1=5-3=7-5=9-7=2$$

The required number is

$$9765-2=9763$$

The greatest number of four digits when divided by 3,5,7,9 leaves remainders 1,3,5,7 respectively is $9763.$