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A number"X" leaves the same reminder while dividing 5814, 5430, 5958. What is the largest possible value of "X" .

**{ Please find the solution with proper explanation and please don't give any weblink or any certified answer}**

So we can write

5814 = a X + y

5430 = b X + y

And 5958 = c X + y

==> (a - b) X = 384

And (c - b) X = 528

Also (c - a) X = 144

Now we have to find the HCF of 384, 528 and 144

It is found to be 48

48 * 8 , 48 * 11 and 48 * 3

Hence maximum value of X is

**48**

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