1.

on dividing a natural number by 13 the remainder is 3 and on dividing a number by 21 the remainder is 11 if the number lies between 500 and 600 then find the number and find the remainder on dividing the number by 19

Answer»

Answer:

The required Number is 536 and remainder is 4.

Step-by-step EXPLANATION:

Let x be the number.

using DIVISION algorithm we get,

x = 21A + 11.

Also, x = 13b + 3

Now let's find the smallest such number.

21a + 11 = 13b + 3.  

21a - 13b = - 8

The smallest a and b which ensures that we get an integer is a = 12 and b = 20. Substitute in above equations and we get the smallest number to be 260.

Now to get the next solution, we can take a=25 and b=41.

So, the number is 536, which as required lies between 500 and 600.

Now DIVIDING 536 by 19.

We get remainder = 4.

Therefore, The required Number is 536 and remainder is 4.


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