Find the least number that will divide 43, 91 and 183 so as to leave the same remainder 4erin each case.

Explanation

To find the least number that will divide 43, 91, and 183 leaving the same remainder in each case, we can follow these steps:

### Step 1: Define the numbers
Let:
- A = 43
- B = 91
- C = 183

### Step 2: Calculate the differences
We need to find the differences between these numbers:
- \( B - A = 91 - 43 = 48 \)
- \( C - B = 183 - 91 = 92 \)
- \( C - A = 183 - 43 = 140 \)

### Step 3: List the differences
Now we have the differences:
- 48
- 92
- 140

### Step 4: Find the HCF of the differences
We need to find the highest common factor (HCF) of the differences 48, 92, and 140.

#### Step 4.1: Prime factorization
- **48**: \( 48 = 2^4 \times 3^1 \)
- **92**: \( 92 = 2^2 \times 23^1 \)
- **140**: \( 140 = 2^2 \times 5^1 \times 7^1 \)

#### Step 4.2: Identify common factors
The common factor in all three numbers is \( 2^2 \).

### Step 5: Calculate the HCF
The HCF is:
- \( 2^2 = 4 \)

### Conclusion
The least number that will divide 43, 91, and 183 leaving the same remainder in each case is **4**.

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