Question

After the division of a number successively by 3, 4, and 7, the remainders obtained are 2, 1 and 4 respectively. What

will be the remainder if 84 divide the same number?​

Answer 1

Answer:

As the Number gives a remainder of 4 when it is divided by 7, then the number must be in form of (7x + 4)

The same gives remainder 1 when it is divided 4, so the number must be in the form of {4 × (7x + 4) + 1}

Also, the number when divided by 3 gives remainder 2, thus number must be in form of [3 × {4 × (7x + 4) + 1} + 2]

Now, On simplifying,

[3 × {4 × (7x + 4) + 1} + 2]

= 84x + 53

We get the final number 53 more than a multiple of 84 Hence, if the number is divided by 84,

The remainder will be 53