To find the HCF of two numbers using prime factorization, list their prime factors, and then multiply the common factors with the lowest exponent.

To find the HCF (Highest Common Factor) of two numbers using prime factorization:

Step 1: Prime factorize both numbers into their prime factors.

Step 2: Identify common prime factors in both numbers.

Step 3: Multiply these common prime factors together to find the HCF.

Example: Let’s find the HCF of 36 and 48.

1. Prime Factorization:

List the prime factors of each number.

• Prime factors of 36: 2²×3²
• Prime factors of 48: 2⁴×3

2. Identify Common Prime Factors:

Identify the prime factors that both numbers share.

• Common prime factors: 2²×3

3. Choose the Lowest Exponent:

For each common prime factor, choose the one with the lowest exponent.

• 2² has an exponent of 2, and 3 has an exponent of 1.

4. Multiply Common Prime Factors:

Multiply the common prime factors with the lowest exponent.

• HCF = 2²×3=12

5. Verify:

Check that 12 is a factor of both 36 and 48.

• 36÷12=3
• 48÷12=4

Conclusion: The HCF of 36 and 48 is 12.