Use Euclid's division algorithm, to find the HCF of 176 and 38220

Answer

To find the HCF (Highest Common Factor) of 176 and 38220 using Euclid's division algorithm, we can follow these steps:

### Step 1: Apply Euclid's Division Algorithm
We start by dividing the larger number (38220) by the smaller number (176).

\[ 38220 \div 176 = 217 \quad \text{(quotient)} \]
\[ 38220 - (176 \times 217) = 38220 - 38232 = -12 \quad \text{(remainder)} \]

Since the remainder is negative, we take the absolute value:

\[ \text{Remainder} = 12 \]

### Step 2: Repeat the Process
Now, we will apply the algorithm again, using 176 and the remainder 12.

\[ 176 \div 12 = 14 \quad \text{(quotient)} \]
\[ 176 - (12 \times 14) = 176 - 168 = 8 \quad \text{(remainder)} \]

### Step 3: Continue Until Remainder is Zero
Next, we repeat the process with 12 and 8.

\[ 12 \div 8 = 1 \quad \text{(quotient)} \]
\[ 12 - (8 \times 1) = 12 - 8 = 4 \quad \text{(remainder)} \]

Now, we continue with 8 and 4.

\[ 8 \div 4 = 2 \quad \text{(quotient)} \]
\[ 8 - (4 \times 2) = 8 - 8 = 0 \quad \text{(remainder)} \]

### Step 4: Conclusion
Since the remainder is now 0, the last non-zero remainder is the HCF. Therefore, the HCF of 176 and 38220 is:

\[ \text{HCF} = 4 \]

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