The HCF of 20, 24 and 48 will be

Options

A. 4
B. 6
C. 5
D. 7

Answer

To find the HCF (Highest Common Factor) of the numbers 20, 24, and 48, we will follow these steps:

### Step 1: Find the Prime Factorization of Each Number
- **For 20**:
- 20 can be divided by 2: \(20 \div 2 = 10\)
- 10 can be divided by 2: \(10 \div 2 = 5\)
- 5 is a prime number.
- So, the prime factorization of 20 is \(2^2 \times 5\).

- **For 24**:
- 24 can be divided by 2: \(24 \div 2 = 12\)
- 12 can be divided by 2: \(12 \div 2 = 6\)
- 6 can be divided by 2: \(6 \div 2 = 3\)
- 3 is a prime number.
- So, the prime factorization of 24 is \(2^3 \times 3\).

- **For 48**:
- 48 can be divided by 2: \(48 \div 2 = 24\)
- 24 can be divided by 2: \(24 \div 2 = 12\)
- 12 can be divided by 2: \(12 \div 2 = 6\)
- 6 can be divided by 2: \(6 \div 2 = 3\)
- 3 is a prime number.
- So, the prime factorization of 48 is \(2^4 \times 3\).

### Step 2: Identify the Common Factors
Now, we will look for the common prime factors in the factorizations:
- The prime factorization of 20 is \(2^2 \times 5\).
- The prime factorization of 24 is \(2^3 \times 3\).
- The prime factorization of 48 is \(2^4 \times 3\).

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

### Step 3: Determine the Lowest Power of Common Factors
- The lowest power of 2 in the factorizations:
- In 20: \(2^2\)
- In 24: \(2^3\)
- In 48: \(2^4\)

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

### Step 4: Calculate the HCF
Now, we calculate the HCF:
- HCF = \(2^2 = 4\)

Thus, the HCF of 20, 24, and 48 is **4**.

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