On dividing 55390 by 299, the remainder is 75. Find the quotient using the division algorithm.

Answer

To solve the problem using the division algorithm, we will follow these steps:

### Step 1: Understand the division algorithm
The division algorithm states that:
\[ \text{Dividend} = (\text{Divisor} \times \text{Quotient}) + \text{Remainder} \]

### Step 2: Identify the given values
From the question:
- Dividend = 55390
- Divisor = 299
- Remainder = 75

### Step 3: Write the equation using the division algorithm
Using the division algorithm, we can write:
\[ 55390 = (299 \times \text{Quotient}) + 75 \]

### Step 4: Rearrange the equation to find the quotient
To find the quotient, we first subtract the remainder from the dividend:
\[ 55390 - 75 = 299 \times \text{Quotient} \]
\[ 55315 = 299 \times \text{Quotient} \]

### Step 5: Divide to find the quotient
Now, we will divide 55315 by 299 to find the quotient:
\[ \text{Quotient} = \frac{55315}{299} \]

Calculating this:
\[ \text{Quotient} = 185 \]

### Step 6: Conclusion
Thus, the quotient when 55390 is divided by 299 with a remainder of 75 is:
\[ \text{Quotient} = 185 \]

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