Find the HCF of 210 , 495 and 980.

Answer

To find the HCF (Highest Common Factor) of the numbers 210, 495, and 980, we can use the continuous division method. Here’s a step-by-step solution:

### Step 1: Choose Two Numbers
We will start by choosing two numbers from the three given numbers. Let's choose 495 and 980.

### Step 2: Perform Division
- **Dividend:** 980 (the larger number)
- **Divisor:** 495 (the smaller number)

Now, we perform the division:
- 980 ÷ 495 = 1 (Quotient)
- Remainder = 980 - (1 × 495) = 980 - 495 = 485

### Step 3: Continue the Division
Now, we will continue the division using the previous divisor and the remainder:
- **New Dividend:** 495
- **New Divisor:** 485

Perform the division:
- 495 ÷ 485 = 1 (Quotient)
- Remainder = 495 - (1 × 485) = 495 - 485 = 10

### Step 4: Continue Again
Next, we continue with the last divisor and the remainder:
- **New Dividend:** 485
- **New Divisor:** 10

Perform the division:
- 485 ÷ 10 = 48 (Quotient)
- Remainder = 485 - (48 × 10) = 485 - 480 = 5

### Step 5: Continue Once More
Now, we continue with the last divisor and the remainder:
- **New Dividend:** 10
- **New Divisor:** 5

Perform the division:
- 10 ÷ 5 = 2 (Quotient)
- Remainder = 10 - (2 × 5) = 10 - 10 = 0

### Step 6: Find HCF of the First Two Numbers
At this point, since the remainder is 0, we find that the HCF of 495 and 980 is 5.

### Step 7: Find HCF with the Third Number
Now we need to find the HCF of the result (5) and the third number (210):
- **Dividend:** 210
- **Divisor:** 5

Perform the division:
- 210 ÷ 5 = 42 (Quotient)
- Remainder = 210 - (42 × 5) = 210 - 210 = 0

### Conclusion
Since the remainder is 0, the HCF of 210 and 5 is 5. Therefore, the HCF of 210, 495, and 980 is **5**.

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