Use Euclid's division algorithm to find the HCF of :
196 and 38220

Answer

To find the HCF (Highest Common Factor) of 196 and 38220 using Euclid's division algorithm, we will follow these steps:

### Step 1: Apply Euclid's Division Algorithm
We start by dividing the larger number (38220) by the smaller number (196).

\[ 38220 \div 196 \]

### Step 2: Perform the Division
Calculating the division gives us:

\[ 38220 \div 196 = 195 \quad \text{(quotient)} \]

Now, we calculate the remainder:

\[ \text{Remainder} = 38220 - (195 \times 196) \]

Calculating \(195 \times 196\):

\[ 195 \times 196 = 38220 \]

Now, substituting back:

\[ \text{Remainder} = 38220 - 38220 = 0 \]

### Step 3: Check the Remainder
Since the remainder is 0, we can conclude that the HCF is the divisor from the last non-zero remainder step, which is 196.

Thus,

\[ \text{HCF}(196, 38220) = 196 \]

### Final Answer
The HCF of 196 and 38220 is **196**.

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