One of the most important and exam oriented question from real numbers in which we have been asked to find the largest four digits number which when divided by 4, 7 and 13 leaves a remainder of 3 in each case.
Kindly give me a detailed solution of this question
RS Aggarwal, Class 10, chapter 1B, question no 14
Prime factors of 4,7 and 13
4=2×2
7 and 13 are prime numbers
LCM (4,7,13)=364
we know that, the largest 4 digit number is 9999.
Step 1 : divide 9999 by 364, we get
9999/364=171
Step 2: subtract 171 from 9999
9999−171=9828
Since a remainder of 3 is to be left
9282+3=9831
therefore 9831 is the number.