Question

find the greatest number which is such that when 12288,19139, and 28200are divided by it, the remainders are all the same​

Answer 1

Answer:

221

Step-by-step explanation:

 Given  

find the greatest number which is such that when 12288,19139, and 28200 are divided by it, the remainders are all the same

Let x be the remainder.

We know that if two numbers be divisible by a certain number, then their difference is also divisible by that number.  

Let the number be 12288 – x , 19139 – x and 28200 – x are exactly divisible by the required number.

We can write it as 19139 – x – (12288 – x) = 6851

                             28200 – x – (19139 – x) = 9061

                             28200 – x – (12288 – x) = 15912

The factors for the number will be  

6851 = 13 x 17 x 31

9061 = 13 x 17 x 41

15912 = 2 x 2 x 2 x 3 x 3 x 13 x 17

G. C. F is 13 x 17 = 221

So the number is 221.  

The remainder can be got by dividing 12288 / 221 = 133.