Find the remainder when 73 *75 *78 *57 *197 is divided by 34.

Property : Product of remainders = Remainder of Product

So let's find the remainder when 73, 75, 78, 59 & 197 are individually divided by 37

This is 5, 7, 10, 23 & 27

So remainder of the product 73 *75 *78 *57 *197 when divided by 37 = Product of 5*7*10*23*27

But note that 5*7*10*23*27 is definitely more than 34 whereas the final remainder should be less than 34 [Any number divided by any other number 'd'can leave remainders from 0 to (d-1) ]

So we can repeat the above steps to arrive at the final remainder which will be less than 34

5*7*10*23*27 = 35*230*27

35 leaves a remainder of 1, 230 leaves a remainder of 26, 27 leaves a remainder of 27

Therefore final remainder = remainder of (1*26*27)/34 or remainder of 702/34 which is 22

Answer is (A)

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