**Euclid's Division Algorithm:**

Euclid's Division Algorithm is a method used to find the Highest Common Factor (HCF) of two or more numbers. It is based on the fact that if we divide a number 'a' by another number 'b' and obtain a remainder 'r', then the HCF of 'a' and 'b' will also be the HCF of 'b' and 'r'. This process is repeated until the remainder becomes zero.

**Step 1: Dividend and Divisor**

Let's start by considering the numbers given: 3, 21, and 396. We will use Euclid's Division Algorithm to find the HCF.

- The first step is to identify the dividend and divisor. In this case, we will take 396 as the dividend and divide it by 21, which will act as the divisor.

**Step 2: Division and Remainder**

- Divide 396 by 21:
- Quotient = 18
- Remainder = 18

**Step 3: Recursion**

- According to Euclid's Division Algorithm, we need to repeat the division process by taking the divisor as the new dividend and the remainder as the new divisor.

- Now, the new dividend is 21 (previous remainder) and the new divisor is 18 (previous divisor).

**Step 4: Repeat Division and Remainder**

- Divide 21 by 18:
- Quotient = 1
- Remainder = 3

**Step 5: Recursion**

- Again, we need to repeat the division process using the new dividend (18) and the new divisor (3).

**Step 6: Final Division and Remainder**

- Divide 18 by 3:
- Quotient = 6
- Remainder = 0

**Step 7: HCF**

- We stop the process when the remainder becomes zero. At this point, the divisor of the previous step is the HCF of the given numbers.

- Therefore, the HCF of 3, 21, and 396 is 3.

In conclusion, by applying Euclid's Division Algorithm, we found that the HCF of 3, 21, and 396 is 3.

396=321×1+75
321=75×4+21
75=21×3+12
21=12×1+9
12=9×1+3
9=3×3+0

HCF of (396, 321 )= 3