Which of the following prime numbers, when dividing 2176, leaves a remainder of 9?

Question

Accepted Answer

To solve this problem, we use the division algorithm. When a number $$ a $$ is divided by $$ b $$, it can be expressed as:  
$$
a = b \cdot q + r
$$
where:  
- $$ a $$ is the dividend (2176 in this case),  
- $$ b $$ is the divisor (the prime number we are looking for),  
- $$ q $$ is the quotient, and  
- $$ r $$ is the remainder (given as 9).

Rewriting this equation:  
$$
b \cdot q = a - r
$$
Substituting $$ a = 2176 $$ and $$ r = 9 $$:  
$$
b \cdot q = 2176 - 9 = 2167
$$

Next, we find the prime factors of 2167. The prime factorization of 2167 is:  
$$
2167 = 11 \cdot 197
$$

Among the given options, only **197** divides 2167 exactly. Therefore, when dividing 2176 by **197**, the remainder is indeed **9**.

Thus, the correct answer is **d) 197**.

Answer

Answer

Answer