a) 79

b) 134

c) 194

d) 234

correct answer is: d) 234

#### Explanation

According to the question,

Three successive remainders are provided which are 49,23 and 4.

So, 1 ^{st} skip the last two digits from the right end of 75118.

\rightarrow This leaves us with 751.

Then, Divide 751 by some number.

\rightarrow We have a remainder of 49.

Next, divide 491 by the same number. _{(bringing down the 1)}

\rightarrow We get 23 as the remainder.

Finally, divide 238 by the same number. _{(bringing down the 8)}

\rightarrow We get 4 as the remainder.

Here,

To find the required divisor, we can use greatest common divisor or (GCD) method.

First, we find the differences between the dividends and remainders.

751-49=702

491-23=468

238-4=234

Now, we find the greatest common divisor (GCD) of 702,468 and 234.

\rightarrow Divide 468 by 234: \left(468\ \div\ 234\ \right) = 2 with a remainder of 0.

\therefore The GCD of 234 and 468 is 234.

\rightarrow Divide 702 by 234: \left(702\ \div\ 234\ \right) = 3 with a remainder of 0.

\therefore The GCD of 234 and 702 is 234.

Therefore, the greatest common divisor of 234,468 and 702 is 234.

So that, the required divisor is 234. **Ans:** The number 234 is the divisor that, when dividing 75118, leaves remainders of 49,23 and 4.

**If dividing 75118 by a certain number results in remainders of 49, 23 and 4 respectively, what is that divisor?****Identify the divisor that, upon dividing 75118, results in remainders of 49, 23 and 4 sequentially.****What is the divisor when 75118 is divided, resulting in remainders of 49, 23 and 4 successively?**