Question

On dividing a natural number by 13, the remainder is 3 and on dividing the same number by 21, the remainder

is 11. Ifthe number lies between 500 and 600, then the remainder on dividing the number by 19 is​

Answer 1

9514 1404 393

Answer:

4

Explanation:

The least common multiple of 13 and 21 is 274, so the number of interest will be 10 less than that. The value in the given range is ...

2(274) -10 = 536

We are interested in the remainder from 536/19, which is 4.

__

536 = 13·41 +3 = 21·25 +11 = 19·28 +4