What is the HCF of 16, 72 and 28 ?

Options

A. 3
B. 4
C. 2
D. 1

Answer

To find the HCF (Highest Common Factor) of the numbers 16, 72, and 28, we will use the method of prime factorization. Here’s the step-by-step solution:

### Step 1: Prime Factorization of Each Number
- **For 16**:
- 16 can be expressed as \(2 \times 8\)
- 8 can be expressed as \(2 \times 4\)
- 4 can be expressed as \(2 \times 2\)
- Therefore, the prime factorization of 16 is:
\[ 16 = 2^4 \]

- **For 72**:
- 72 can be expressed as \(2 \times 36\)
- 36 can be expressed as \(2 \times 18\)
- 18 can be expressed as \(2 \times 9\)
- 9 can be expressed as \(3 \times 3\)
- Therefore, the prime factorization of 72 is:
\[ 72 = 2^3 \times 3^2 \]

- **For 28**:
- 28 can be expressed as \(2 \times 14\)
- 14 can be expressed as \(2 \times 7\)
- Therefore, the prime factorization of 28 is:
\[ 28 = 2^2 \times 7 \]

### Step 2: Identify Common Prime Factors
Now we will identify the common prime factors among the three numbers:
- The prime factors of 16 are \(2^4\).
- The prime factors of 72 are \(2^3 \times 3^2\).
- The prime factors of 28 are \(2^2 \times 7\).

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

### Step 3: Determine the Lowest Power of Common Factors
Now we take the lowest power of the common prime factor:
- For \(2\), the powers are:
- In 16: \(2^4\)
- In 72: \(2^3\)
- In 28: \(2^2\)

The lowest power of \(2\) is \(2^2\).

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

### Final Answer
The HCF of 16, 72, and 28 is **4**.

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