The difference between the sum of prime numbers from $21$ to $30$ and the sum of composite from $21$ to $30$ is divisible by which of the following numbers?

The correct option is C

$151$

Determine the number that divides difference between the sum of prime numbers from $21$ to $30$ and the sum of composite from $21$ to $30$ :

Explanation of the correct option.

The prime numbers from $21$ to $30$ are $23\mathrm{and}29$.

So, the sum of these prime numbers is:

$23+29=52$

The composite numbers from $21$ to $30$ are $21,22,24,25,26,27,28,\mathrm{and}30$.

The sum of these composite numbers is:

$21+22+24+25+26+27+28+30=203$

The difference between the sum of prime and composite numbers is:

$203-52=151$

The number $151$ is a prime number.

So, it is divisible by $1\mathrm{and}151$.

Thus, option (C) is the correct option.

Explanation of incorrect options.

The number $151$ is a prime number so it cannot be divisible by $3,7,\mathrm{or}17$.

So, options (A), (B), and (D) are incorrect.

Hence, option (C) is the correct option.