Find the Greatest Common Factor of 28 and 144
A. 2
B. 8
C. 6
D. 4

Options

A. B
B. D
C. A
D. C

Answer

To find the Greatest Common Factor (GCF) of 28 and 144, we can use the prime factorization method. Here are the steps:

### Step 1: Prime Factorization of 28
- Start by dividing 28 by the smallest prime number, which is 2.
- 28 ÷ 2 = 14
- 14 ÷ 2 = 7
- 7 is a prime number, so we stop here.

Thus, the prime factorization of 28 is:
\[ 28 = 2^2 \times 7^1 \]

### Step 2: Prime Factorization of 144
- Start by dividing 144 by the smallest prime number, which is 2.
- 144 ÷ 2 = 72
- 72 ÷ 2 = 36
- 36 ÷ 2 = 18
- 18 ÷ 2 = 9
- 9 ÷ 3 = 3
- 3 is a prime number, so we stop here.

Thus, the prime factorization of 144 is:
\[ 144 = 2^4 \times 3^2 \]

### Step 3: Identify Common Factors
- Now, we will identify the common prime factors from the factorizations of 28 and 144.
- The prime factors of 28 are \( 2^2 \) and \( 7^1 \).
- The prime factors of 144 are \( 2^4 \) and \( 3^2 \).
- The only common prime factor is \( 2 \).

### Step 4: Determine the Lowest Power of Common Factors
- For the common prime factor \( 2 \), we take the lowest power from both factorizations.
- From 28, the power of 2 is \( 2^2 \) and from 144, the power of 2 is \( 2^4 \).
- The lowest power is \( 2^2 \).

### Step 5: Calculate the GCF
- Now, we calculate the GCF by multiplying the common prime factors raised to their lowest powers.
\[ GCF = 2^2 = 4 \]

Thus, the Greatest Common Factor of 28 and 144 is **4**.

### Final Answer
The correct option is **D. 4**.

---