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 can 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 also be divided by 2:
- \( 10 \div 2 = 5 \)
- 5 is a prime number.
- Thus, the prime factorization of 20 is:
- \( 20 = 2^2 \times 5^1 \)

- **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.
- Thus, the prime factorization of 24 is:
- \( 24 = 2^3 \times 3^1 \)

- **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.
- Thus, the prime factorization of 48 is:
- \( 48 = 2^4 \times 3^1 \)

### Step 2: Identify the Common Factors
Now we will look for the common prime factors in all three numbers:
- The prime factors of 20 are \( 2^2 \times 5^1 \)
- The prime factors of 24 are \( 2^3 \times 3^1 \)
- The prime factors of 48 are \( 2^4 \times 3^1 \)

The only common prime factor is 2.

### Step 3: Determine the Lowest Power of the Common Factors
- The lowest power of the common factor (2) in the factorizations is:
- For 20: \( 2^2 \)
- For 24: \( 2^3 \)
- For 48: \( 2^4 \)
- The lowest power 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**.

### Final Answer
The HCF of 20, 24, and 48 is **4**.

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