What will be the HCF of 56, 216, 28 ?

Options

A. 28
B. 2
C. 8
D. 4

Answer

To find the HCF (Highest Common Factor) of the numbers 56, 216, and 28, we can use the factorization method. Here’s a step-by-step solution:

### Step 1: Factorize each number
- **Factorizing 56**:
- 56 can be divided by 2:
- 56 ÷ 2 = 28
- 28 ÷ 2 = 14
- 14 ÷ 2 = 7
- 7 is a prime number.
- Therefore, the prime factorization of 56 is:
\[ 56 = 2^3 \times 7^1 \]

- **Factorizing 216**:
- 216 can be divided by 2:
- 216 ÷ 2 = 108
- 108 ÷ 2 = 54
- 54 ÷ 2 = 27
- 27 can be divided by 3:
- 27 ÷ 3 = 9
- 9 ÷ 3 = 3
- 3 ÷ 3 = 1
- Therefore, the prime factorization of 216 is:
\[ 216 = 2^3 \times 3^3 \]

- **Factorizing 28**:
- 28 can be divided by 2:
- 28 ÷ 2 = 14
- 14 ÷ 2 = 7
- 7 is a prime number.
- Therefore, the prime factorization of 28 is:
\[ 28 = 2^2 \times 7^1 \]

### Step 2: Identify the common factors
Now, we will identify the common prime factors from the factorizations:
- **56**: \(2^3 \times 7^1\)
- **216**: \(2^3 \times 3^3\)
- **28**: \(2^2 \times 7^1\)

The common prime factor among all three numbers is \(2\).

### Step 3: Determine the lowest power of the common factors
- The lowest power of \(2\) in the factorizations is \(2^2\) (from 28).

### Step 4: Calculate the HCF
Thus, the HCF is:
\[ HCF = 2^2 = 4 \]

### Final Answer
The HCF of 56, 216, and 28 is **4**.

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