Find the HCF of the numbers in each of the following, using the division method :
391, 425, 527

Answer

To find the HCF (Highest Common Factor) of the numbers 391, 425, and 527 using the division method, we can follow these steps:

### Step 1: Divide the largest number by the smallest number
We start by dividing the largest number (527) by the smallest number (391).

\[ 527 \div 391 = 1 \quad \text{(Quotient)} \]
\[ \text{Remainder} = 527 - (1 \times 391) = 527 - 391 = 136 \]

### Step 2: Repeat the process
Now, we take the divisor (391) and the remainder (136) and repeat the division.

\[ 391 \div 136 = 2 \quad \text{(Quotient)} \]
\[ \text{Remainder} = 391 - (2 \times 136) = 391 - 272 = 119 \]

### Step 3: Continue with the new divisor and remainder
Next, we take 136 and 119.

\[ 136 \div 119 = 1 \quad \text{(Quotient)} \]
\[ \text{Remainder} = 136 - (1 \times 119) = 136 - 119 = 17 \]

### Step 4: Keep going until the remainder is zero
Now we take 119 and 17.

\[ 119 \div 17 = 7 \quad \text{(Quotient)} \]
\[ \text{Remainder} = 119 - (7 \times 17) = 119 - 119 = 0 \]

### Step 5: Identify the HCF
When the remainder becomes zero, the last non-zero remainder is the HCF. Here, the last non-zero remainder is 17.

Thus, the HCF of 391, 425, and 527 is **17**.

### Step 6: Check if HCF divides the third number
Now, we need to check if 17 divides the third number (425).

\[ 425 \div 17 = 25 \quad \text{(Quotient)} \]
\[ \text{Remainder} = 425 - (25 \times 17) = 425 - 425 = 0 \]

Since the remainder is zero, 17 is indeed the HCF of all three numbers.

### Final Answer:
The HCF of 391, 425, and 527 is **17**.

---