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# Find the remainder when 73 × 75 × 78 × 57 × 197 × 37 is divided by 34.

A. 32

B. 30

C. 15

D. 28

### Solution(By Examveda Team)

Remainder,
$$\frac{{73 \times 75 \times 78 \times 57 \times 197 \times 37}}{{34}}$$
$$= \frac{{5 \times 7 \times 10 \times 23 \times 27 \times 3}}{{34}}$$
[We have taken individual remainder, which means if 73 is divided by 34 individually, it will give remainder 5, 75 divided 34 gives remainder 7 and so on.]

\eqalign{ & \frac{{5 \times 7 \times 10 \times 23 \times 27 \times 3}}{{34}} \cr & = \frac{{35 \times 30 \times 23 \times 27}}{{34}} \cr & = \frac{{1 \times - 4 \times - 11 \times - 7}}{{34}} \cr}

[We have taken here negative as well as positive remainder at the same time. When 30 divided by 34 it will give either positive remainder 30 or negative remainder -4. We can use any one of negative or positive remainder at any time.]

\eqalign{ & \frac{{1 \times - 4 \times - 11 \times - 7}}{{34}} \cr & = \frac{{28 \times - 11}}{{34}} \cr & = \frac{{ - 6 \times - 11}}{{34}} \cr & = \frac{{66}}{{34}} \cr & {\text{R}} = 32 \cr}
Required remainder = 32

1. Understood the math

2. Sir please shoot your video then it would be easy to understand

3. First divide all the number by 34 after getting the remainder multiplying all the remainder and then divide that by 34

4. nice

5. Pls explain easily...&how to come answr with minus in this solution...

6. we have to multipy the unit digits of all the given numbers. we got 0 as the unit digit. And we have to divide with the unit digit of 34 i.e. 4 and obviously, we will get the reminder as 2.The only option having unit digit as 2 is option A.

7. Can you explain short trick for such type of questions

8. kindly someone pls explain me why minus came into picture

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