Find the largest four-digit number which when divided by 4, 7 and 13 leaves a remainder of 3 in each case.

Foundation

Mathematics Foundation

HCF and LCM

Properties of Real Number

Sum of n terms of an AP

Question

Find the largest four-digit number which when divided by 4, 7 and 13 leaves a remainder of 3 in each case.

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Prime factors of 4,7 and 13
$4 = 2 \times 2$
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
$\frac{9999}{,} 364 = 171$
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.