You can find the Highest Common Factor (HCF) of two numbers by identifying the common factors in their prime factorization and multiplying them together. This approach is based on finding the shared elements in the prime factor lists of both numbers.
Here's a step-by-step breakdown using the information from the reference:
- Prime Factorization: Find the prime factors of each number.
- Identify Common Factors: List the prime factors that appear in both lists.
- Multiply Common Factors: The HCF is the product of multiplying all the common prime factors.
Example:
Let's find the HCF of 60 and 72.
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Prime Factorization:
- 60 = 2 × 2 × 3 × 5
- 72 = 2 × 2 × 2 × 3 × 3
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Identify Common Factors: The factors that appear in both lists are 2, 2, and 3.
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Multiply Common Factors: HCF (60, 72) = 2 × 2 × 3 = 12
Therefore, the HCF of 60 and 72 is 12, as derived by multiplying the common prime factors found in the prime factorizations of both numbers. The reference states: "The highest common factor is found by multiplying all the factors which appear in both lists: So the HCF of 60 and 72 is 2 × 2 × 3 which is 12."
