Question

The greatest number of four digits which when divided by 3,5,79 leave remainders 1.3.5.7 respecte
1) 9763
2) 9764
3) 9766
4) 9765​

Answer 1

Answer:

We know largest four digit number = 9999

Answer 2

Solution :-

Here, we have to find the greatest four digit number which when divided 3 , 5 , 7 and 9 leave remainders 1 , 3 , 5 and 7

Now,

As we know that,

The largest four digit number is 9999

Now,

LCM of 3 , 5 , 7 and 9 = 3 * 3 * 5 * 7 = 315

Therefore,

9999 / 315 = 31.74

Now,

According to the question,

= 315 * 31

[ Here, we have taken 31 because we want a number less than 9999]

= 9765

But,

We also observed that,

In each case we get a difference 2

3 - 1 = 2

5 - 3 = 2

7 - 5 = 2

9 - 7 = 2

Therefore,

= 9765 - 2 = 9763

Hence, The largest four digit number which when divided by 3 , 5 , 7 and 9 leave a remainder 1 , 3 , 5 and 7 is 9763 $.$