Question

If the numbers 23794 and 25273 are divided by a number x such that 50<x>100, than the remainder in each case is Y. Find Value of (x-y)?​

Answer 1

Step-by-step explanation:

divisor is 87 and remainder is 43

Answer 2

The value of (x-y)=23 or 44

Step-by-step explanation:

Euclidean algorithm

$a=bq+r$

Where a=Dividend

b=Divisor

q=Quotient

r=Remainder

where $0\leq r<b$

Using Euclidean algorithm

$23794=ax+y$

$25273=bx+y$

$1479=(b-a)x$

1479 is also divisible by x

$1479=3\times 17\times 29=51\times 29\;or 17\times 87$

But $50<x<100$

Therefore, Possible value of x=51 or 87

$23794=51\times 466 +28$

$25273=51\times 495+28$

$25273=87\times 290+43$

Hence, the possible values of y are 28 or 43

When x=51 and y=28

$x-y=51-28=23$

When x=87 and y=43

or$x-y=87-43=44$

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