Find the biggest number which divides 729 & 901 & leaves remainder 9 and 5 respectively?

Options

A. 15
B. 16
C. 19
D. 20

Answer

To find the biggest number that divides 729 and 901 while leaving remainders of 9 and 5 respectively, we can follow these steps:

### Step 1: Subtract the remainders from the numbers
We need to adjust the numbers by subtracting the remainders:
- For 729, subtract 9:
\[ 729 - 9 = 720 \]
- For 901, subtract 5:
\[ 901 - 5 = 896 \]

### Step 2: Find the HCF (Highest Common Factor) of the adjusted numbers
Now we need to find the HCF of 720 and 896. We can use the long division method for this.

1. **Divide 896 by 720**:
\[ 896 \div 720 = 1 \quad \text{(quotient)} \]
Remainder:
\[ 896 - 720 \times 1 = 176 \]

2. **Now divide 720 by the remainder 176**:
\[ 720 \div 176 = 4 \quad \text{(quotient)} \]
Remainder:
\[ 720 - 176 \times 4 = 720 - 704 = 16 \]

3. **Next, divide 176 by the new remainder 16**:
\[ 176 \div 16 = 11 \quad \text{(quotient)} \]
Remainder:
\[ 176 - 16 \times 11 = 176 - 176 = 0 \]

### Step 3: Conclusion
Since the last non-zero remainder is 16, the HCF of 720 and 896 is 16. Therefore, the biggest number that divides 729 and 901 while leaving remainders of 9 and 5 respectively is:
\[ \text{HCF} = 16 \]

### Final Answer:
The biggest number is **16**.

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