Finding the Divisor

This problem requires finding the divisor using the fundamental relationship between the dividend, divisor, quotient, and remainder in division.

Division Algorithm Formula

The relationship is defined by the division algorithm:

$Dividend = (Divisor × Quotient) + Remainder$

In this problem, we have:

• Dividend = 15,971
• Quotient = 55
• Remainder = 21
• Divisor = Let's denote this as $D$

Applying the Formula to Find Divisor

Substitute the given values into the division algorithm formula:

$15,971 = (D \times 55) + 21$

Solving for the Divisor

To find the divisor $D$, first isolate the term involving $D$ by subtracting the remainder from both sides of the equation:

$15,971 - 21 = D \times 55$

$15,950 = D \times 55$

Next, divide the result by the quotient (55) to determine the value of the divisor $D$:

$D = \frac{15,950}{55}$

Performing the division calculation:

$D = 290$

Thus, the divisor is 290.