Use Euclid's division algorithm to find the HCF of :
135 and 225

Answer

To find the HCF (Highest Common Factor) of 135 and 225 using Euclid's division algorithm, we will follow these steps:

### Step 1: Identify the larger and smaller numbers
We have two numbers: 135 and 225. Here, 225 is greater than 135.

### Step 2: Apply Euclid's Division Algorithm
We will divide the larger number (225) by the smaller number (135) and find the remainder.

\[ 225 \div 135 = 1 \quad \text{(quotient)} \]
\[ \text{Remainder} = 225 - (135 \times 1) = 225 - 135 = 90 \]

### Step 3: Repeat the process
Now, we will take the previous divisor (135) and the remainder (90) and apply the division algorithm again.

\[ 135 \div 90 = 1 \quad \text{(quotient)} \]
\[ \text{Remainder} = 135 - (90 \times 1) = 135 - 90 = 45 \]

### Step 4: Continue until the remainder is 0
Next, we take the last divisor (90) and the new remainder (45).

\[ 90 \div 45 = 2 \quad \text{(quotient)} \]
\[ \text{Remainder} = 90 - (45 \times 2) = 90 - 90 = 0 \]

### Step 5: Conclusion
Since the remainder is now 0, the last non-zero remainder (which is 45) is the HCF of 135 and 225.

\[ \text{HCF}(135, 225) = 45 \]

### Final Answer:
The HCF of 135 and 225 is **45**.

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