Question

Find the quotient and the remainder when the largest 7- digit is divided by the largest 2-6 number​

Answer 1

Answer:

Did anyone mention the base used for the numerical representations?

Let’s do this in any integer base b≥2.

The largest seven digit number is b7−1.

The largest three digit number is b3−1.

We can do the following algebra (this is polynomial division):

b7–1 = (b4)(b3−1)+b4−1

= (b4)(b3−1)+b(b3−1)+b−1

= (b4+b)(b3−1)+b−1

So when b7−1 is divided by b3−1 the quotient is b4+b and the remainder is b−1.

I will leave it to you to calculate the quotient and remainder with b=10.

Answer 2

Answer:

Let’s do this in any integer base b≥2.

The largest seven digit number is b7−1.

The largest three digit number is b3−1.

We can do the following algebra (this is polynomial division):

b7–1 = (b4)(b3−1)+b4−1

= (b4)(b3−1)+b(b3−1)+b−1

= (b4+b)(b3−1)+b−1

So when b7−1 is divided by b3−1 the quotient is b4+b and the remainder is b−1.

I will leave it to you to calculate the quotient and remainder with b=10.