Question

A number when divided by 5 and 7 successively,
leaves the remainders 2 and 4 respectively. Find the
remainder when the same number is divided by
35.​

Answer 1

Answer:

No(1)Overall we can solve this using remainder understanding. Here we use successive division for this.

In this case as number was successively divided by 5 and 7 leaving remainders 3 & 5 respectively.

If a number leaves remainder 3 when divided by 5, then it can be expressed as (5p+3). Now 'p' is the quotient after first division.

When ‘p' is divided by 7, it leaves remainder 4.

So, ‘p' can be expressed as (7q+4)

Thus the number should be: [5 x (7q+4) + 3] = (35k + 23)

Now when the number is divided by 35, the remainder will be:

R[(35k+23)/35]

= R[(35k)/35] + R[23/35]

= 0 + 23