Question

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 1

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.