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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

Answer: Option A

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

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Comments ( 8 )

  1. Bishal Saren
    Bishal Saren :
    8 months ago

    Understood the math

  2. Sukhdev Chandrahas
    Sukhdev Chandrahas :
    9 months ago

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

  3. Phernaki Mawlong
    Phernaki Mawlong :
    1 year ago

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

  4. Anju Napit
    Anju Napit :
    2 years ago

    nice

  5. Maha Lakshmi
    Maha Lakshmi :
    2 years ago

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

  6. Raj Kumar
    Raj Kumar :
    2 years ago

    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. SONALI CHOUHAN
    SONALI CHOUHAN :
    2 years ago

    Can you explain short trick for such type of questions

  8. Ami Raheja
    Ami Raheja :
    2 years ago

    kindly someone pls explain me why minus came into picture

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