The HCF of 20, 24 and 26 is

Options

A. 2
B. 3
C. 4
D. 5

Answer

To find the HCF (Highest Common Factor) of the numbers 20, 24, and 26 using prime factorization, we can follow these steps:

### Step-by-Step Solution:

1. **Prime Factorization of 20**:
- We start with the number 20.
- Divide 20 by the smallest prime number, which is 2:
- \( 20 \div 2 = 10 \)
- Divide 10 by 2 again:
- \( 10 \div 2 = 5 \)
- Now, 5 is a prime number.
- Therefore, the prime factorization of 20 is:
\[ 20 = 2^2 \times 5 \]

2. **Prime Factorization of 24**:
- Next, we factor 24.
- Divide 24 by 2:
- \( 24 \div 2 = 12 \)
- Divide 12 by 2:
- \( 12 \div 2 = 6 \)
- Divide 6 by 2:
- \( 6 \div 2 = 3 \)
- Now, 3 is a prime number.
- Therefore, the prime factorization of 24 is:
\[ 24 = 2^3 \times 3 \]

3. **Prime Factorization of 26**:
- Now, we factor 26.
- Divide 26 by 2:
- \( 26 \div 2 = 13 \)
- Now, 13 is a prime number.
- Therefore, the prime factorization of 26 is:
\[ 26 = 2^1 \times 13 \]

4. **Finding the HCF**:
- Now that we have the prime factorizations:
- \( 20 = 2^2 \times 5 \)
- \( 24 = 2^3 \times 3 \)
- \( 26 = 2^1 \times 13 \)
- We need to find the common factors in all three numbers.
- The only common prime factor is 2.
- The lowest power of 2 in the factorizations is \( 2^1 \).
- Therefore, the HCF is:
\[ HCF = 2^1 = 2 \]

5. **Conclusion**:
- The HCF of 20, 24, and 26 is **2**.