To find the Highest Common Factor (HCF) using the common factor method, which is often referred to as the prime factorization method, you follow these steps:
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Prime Factorization: Begin by expressing each of the numbers you are working with as a product of their prime factors. This is sometimes known as prime factorization.
- For example, if you want to find the HCF of 12 and 18:
- 12 = 2 x 2 x 3 or 22 x 3
- 18 = 2 x 3 x 3 or 2 x 32
- For example, if you want to find the HCF of 12 and 18:
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Identify Common Prime Factors: Next, list the prime factors that are common to all the numbers you are analyzing.
- In our example, the common prime factors of 12 and 18 are 2 and 3.
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Determine the Lowest Powers of the Common Factors: For each common prime factor, take the lowest power it is raised to among all the factorizations.
- For the common prime factor 2, the lowest power is 21 (from the factorization of 18).
- For the common prime factor 3, the lowest power is 31 (from the factorization of 12).
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Calculate the HCF: Finally, multiply these common prime factors together, using their lowest powers as determined in the previous step. The product will be the HCF.
- In our example, HCF(12, 18) = 21 x 31= 2 x 3 = 6.
Therefore, the Highest Common Factor (HCF) of 12 and 18 is 6.
In essence, the common factor method for finding the HCF involves breaking numbers down to their prime factors, identifying common factors, and then multiplying those factors together, each raised to its lowest power to produce the HCF.
