tougher problems in HCF and LCM

                                                                                                                                                                                               

The numbers 11284 and 7655, when divided by a certain number of three digits, leave the same remainder. Find the number and the remainder.

                                                                                                                                                                                               

Answer:

Let, Y be the common remainder. So, we have 11284 – y , 7655 – y as the perfectly divisible numbers.

If 2 numbers are exactly divisible by a certain number, then there difference is also exactly divisible.

So, (11284 – y) – (7655 – y), is exactly divisible.

Or, 3629 is divisible by the required number. Let us find the factors of 3629.

We have, 3629 = 191 x 19

Therefore the 3 digit number is 191.

Now let us divide 11284 by 191 to find the remainder

11284/191 = 59 ¹⁵/₁₉₁.

Therefore, the remainder is 15.