Question

let's find the gratest number, which will devide both 540 and 630 to keep remainder 3 in both cases.​

Answer 1

Answer:

The number divides 399,434 and 537 leaving the remainder 8,9 and 10.

So, that number will divide (399−8),(434−9) and (537−10) completely.

Now, the greatest number that will divide 391,425 and 527 completely, is the H.C.F. of these numbers.

391=17×23

425=5×5×17

527=17×31

H.C.F. =17

Answer 2

Answer:

dividing a number x by y leaves a remainder 3, that means that y - 3 will be perfectly divisible by x.

So in this case, we need to find the highest common factor of 561 (564 - 3) and 627 (630 - 3).

Factorising the two numbers:

561 = 3 × 11 × 17

627 = 3 × 11 × 19

We can see that the highest common factor here is 3 × 11 = 33. That is the answer to the question.