Question

If a number is divided by 9, what is the greatest remainder it can leave?

Answer 1

8

The largest remainder that can be left when a number is divided by 9 is 8.

Answer 2

The greatest remainder it can leave = 8

Given :

A number is divided by 9

To find :

The greatest remainder it can leave

Solution :

Step 1 of 2 :

Write down the divisior

Here it is given that a number is divided by 9

So divisor is 9

Step 2 of 2 :

Find greatest remainder it can leave

The division algorithm for integers states that for given any two integers a and b, with b > 0, we can find integers q and r such that 0 ≤ r < b and a = bq + r

Since the number is divided by 9

∴ b = 9

Thus the remainder r is given by 0 ≤ r < 9

∴ r can be any of 0 , 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8

Now the greatest of 0 , 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 is 8

Hence the greatest remainder it can leave is 9

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