To find the H.C.F (Highest Common Factor) of the numbers 20, 16, 12, and 2, we will follow these steps:
### Step 1: Prime Factorization of Each Number
- **20**:
- 20 can be factored as \( 20 = 2 \times 10 = 2 \times 2 \times 5 \)
- So, the prime factorization of 20 is \( 2^2 \times 5^1 \).
- **16**:
- 16 can be factored as \( 16 = 2 \times 8 = 2 \times 2 \times 4 = 2 \times 2 \times 2 \times 2 \)
- So, the prime factorization of 16 is \( 2^4 \).
- **12**:
- 12 can be factored as \( 12 = 2 \times 6 = 2 \times 2 \times 3 \)
- So, the prime factorization of 12 is \( 2^2 \times 3^1 \).
- **2**:
- 2 is already a prime number.
- So, the prime factorization of 2 is \( 2^1 \).
### Step 2: Identify Common Prime Factors
Now, we will identify the common prime factors from the factorizations:
- The common prime factor among 20, 16, 12, and 2 is \( 2 \).
### Step 3: Determine the Lowest Power of Common Factors
Next, we find the lowest power of the common prime factor:
- For \( 2 \):
- In 20: \( 2^2 \)
- In 16: \( 2^4 \)
- In 12: \( 2^2 \)
- In 2: \( 2^1 \)
The lowest power of \( 2 \) is \( 2^1 \).
### Step 4: Calculate the H.C.F
Thus, the H.C.F of 20, 16, 12, and 2 is:
\[
\text{H.C.F} = 2^1 = 2
\]
### Final Answer
The H.C.F of 20, 16, 12, and 2 is **2**.
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