Find the HCF of 6 and 20.
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Step-by-Step Solution
Step 1: Prime Factorization of the first number
First, we find the prime factorization of 6. This means expressing 6 as a product of its prime factors. The prime factors of 6 are 2 and 3.
Step 2: Prime Factorization of the second number
Next, we find the prime factorization of 20. This means expressing 20 as a product of its prime factors. The prime factors of 20 are 2, 2, and 5, which can be written as 22×5.
Step 3: Identify common prime factors with the smallest power
To find the HCF, we identify the prime factors common to both 6 and 20. The only common prime factor is 2. We then take the smallest power of this common prime factor from its occurrences in both numbers. For 2, the powers are 21 (from 6) and 22 (from 20). The smallest power is 21.
Step 4: Calculate the HCF
The HCF is the product of the smallest power of each common prime factor. In this case, the only common prime factor raised to its smallest power is 21, which equals 2. Therefore, the HCF of 6 and 20 is 2.