Use Euclid's division algorithm to find the HCF of 16 and 28.

Answer

To find the HCF (Highest Common Factor) of 16 and 28 using Euclid's division algorithm, we will follow these steps:

### Step 1: Identify the numbers
We have two numbers:
- A = 28
- B = 16

### Step 2: Apply Euclid's division algorithm
According to Euclid's division algorithm, we can express A in terms of B and the remainder R:
\[ A = B \cdot Q + R \]
Where:
- A is the larger number (28)
- B is the smaller number (16)
- Q is the quotient
- R is the remainder

### Step 3: Perform the first division
Now we divide 28 by 16:
\[ 28 = 16 \cdot 1 + R \]
Calculating:
- Quotient (Q) = 1
- Remainder (R) = 28 - (16 * 1) = 28 - 16 = 12

So, we can write:
\[ 28 = 16 \cdot 1 + 12 \]

### Step 4: Repeat the process
Now we take B (16) and the remainder (12) and apply the algorithm again:
\[ 16 = 12 \cdot Q + R \]
Calculating:
- Quotient (Q) = 1
- Remainder (R) = 16 - (12 * 1) = 16 - 12 = 4

So, we can write:
\[ 16 = 12 \cdot 1 + 4 \]

### Step 5: Continue until remainder is 0
Next, we take 12 and the remainder (4):
\[ 12 = 4 \cdot Q + R \]
Calculating:
- Quotient (Q) = 3
- Remainder (R) = 12 - (4 * 3) = 12 - 12 = 0

So, we can write:
\[ 12 = 4 \cdot 3 + 0 \]

### Step 6: Identify the HCF
When the remainder becomes 0, the last non-zero remainder is the HCF. Here, the last non-zero remainder is 4.

Thus, the HCF of 16 and 28 is:
\[ \text{HCF} = 4 \]

### Final Answer:
The HCF of 16 and 28 is 4.

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