Find the HCF of 12, 20 and 32.

Answer

To find the HCF (Highest Common Factor) of the numbers 12, 20, and 32, we can follow these steps:

### Step 1: Find the Prime Factorization of Each Number
- **12**: The prime factorization of 12 is \(2^2 \times 3^1\).
- **20**: The prime factorization of 20 is \(2^2 \times 5^1\).
- **32**: The prime factorization of 32 is \(2^5\).

### Step 2: Identify Common Prime Factors
Next, we look for the common prime factors among the three numbers:
- The only common prime factor is \(2\).

### Step 3: Determine the Lowest Power of the Common Prime Factor
Now, we take the lowest power of the common prime factor:
- For \(2\), the powers are:
- In 12: \(2^2\)
- In 20: \(2^2\)
- In 32: \(2^5\)

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

### Step 4: Calculate the HCF
Now, we calculate the HCF using the lowest power of the common prime factor:
- HCF = \(2^2 = 4\).

Thus, the HCF of 12, 20, and 32 is **4**.

---