Find the maximum number which divides 2300 & 3500 and leaves remainder 32 and 56 respectively ?

Options

A. 136
B. 168
C. 42
D. 84

Answer

To find the maximum number that divides 2300 and 3500 while leaving remainders of 32 and 56 respectively, we can follow these steps:

### Step 1: Subtract the remainders from the original numbers.
- For 2300, subtract the remainder 32:
\[ 2300 - 32 = 2268 \]
- For 3500, subtract the remainder 56:
\[ 3500 - 56 = 3444 \]

### Step 2: Find the HCF (Highest Common Factor) of the two results (2268 and 3444).
We will use the long division method to find the HCF.

1. Divide the larger number by the smaller number:
\[ 3444 \div 2268 \quad \text{(the quotient is 1, remainder is 1176)} \]
\[ 3444 = 2268 \times 1 + 1176 \]

2. Now, take the previous divisor (2268) and divide it by the remainder (1176):
\[ 2268 \div 1176 \quad \text{(the quotient is 1, remainder is 1092)} \]
\[ 2268 = 1176 \times 1 + 1092 \]

3. Next, take 1176 and divide it by 1092:
\[ 1176 \div 1092 \quad \text{(the quotient is 1, remainder is 84)} \]
\[ 1176 = 1092 \times 1 + 84 \]

4. Now, take 1092 and divide it by 84:
\[ 1092 \div 84 \quad \text{(the quotient is 13, remainder is 0)} \]
\[ 1092 = 84 \times 13 + 0 \]

Since the remainder is now 0, the last non-zero remainder is the HCF. Therefore, the HCF of 2268 and 3444 is 84.

### Step 3: Conclusion
The maximum number that divides 2300 and 3500, leaving remainders of 32 and 56 respectively, is **84**.

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