Find the HCF of 144 and 196 by using long division method.

Answer

To find the HCF (Highest Common Factor) of 144 and 196 using the long division method, we can follow these steps:

### Step 1: Set up the division
Since 144 is less than 196, we will divide 196 by 144.

### Step 2: Perform the division
1. Divide 196 by 144.
- 144 goes into 196 one time (1).
- Multiply 1 by 144 to get 144.
- Subtract 144 from 196:
\[ 196 - 144 = 52 \]
- So, we have:
\[ 196 = 144 \times 1 + 52 \]

### Step 3: Repeat the process
Now, take the remainder (52) and divide the previous divisor (144) by this remainder (52).

1. Divide 144 by 52.
- 52 goes into 144 two times (2).
- Multiply 2 by 52 to get 104.
- Subtract 104 from 144:
\[ 144 - 104 = 40 \]
- So, we have:
\[ 144 = 52 \times 2 + 40 \]

### Step 4: Continue the division
Now, take the remainder (40) and divide the previous divisor (52) by this remainder (40).

1. Divide 52 by 40.
- 40 goes into 52 one time (1).
- Multiply 1 by 40 to get 40.
- Subtract 40 from 52:
\[ 52 - 40 = 12 \]
- So, we have:
\[ 52 = 40 \times 1 + 12 \]

### Step 5: Keep going
Now, take the remainder (12) and divide the previous divisor (40) by this remainder (12).

1. Divide 40 by 12.
- 12 goes into 40 three times (3).
- Multiply 3 by 12 to get 36.
- Subtract 36 from 40:
\[ 40 - 36 = 4 \]
- So, we have:
\[ 40 = 12 \times 3 + 4 \]

### Step 6: Final division
Now, take the remainder (4) and divide the previous divisor (12) by this remainder (4).

1. Divide 12 by 4.
- 4 goes into 12 three times (3).
- Multiply 3 by 4 to get 12.
- Subtract 12 from 12:
\[ 12 - 12 = 0 \]
- So, we have:
\[ 12 = 4 \times 3 + 0 \]

### Step 7: Conclusion
Since we have reached a remainder of 0, the last non-zero remainder is the HCF. Therefore, the HCF of 144 and 196 is **4**.

### Final Answer:
The HCF of 144 and 196 is **4**.

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