What is the highest common factor of 15 and 20

General
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what is the highest common factor of 15 and 20

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What is the highest common factor of 15 and 20?

Answer: The highest common factor (HCF), also known as the greatest common divisor (GCD), of two numbers is the largest number that divides both of them without leaving a remainder. To find the HCF of 15 and 20, we can use the following methods:

Method 1: Prime Factorization

  1. Prime Factorize each Number:

    • The prime factorization of 15 is (15 = 3 \times 5).
    • The prime factorization of 20 is (20 = 2^2 \times 5).

  2. Identify the Common Factors:

    • The common prime factor of 15 and 20 is (5).

  3. Multiply the Common Factors:

    • The highest common factor (HCF) is (5).

Method 2: Euclidean Algorithm

The Euclidean algorithm is a process for finding the HCF by repeatedly applying the division algorithm. Here’s how:

  1. Apply the Division Algorithm:

    • Divide the larger number by the smaller number and take the remainder.
    • Replace the larger number with the smaller number and the smaller number with the remainder.
    • Repeat the steps until the remainder is 0. The non-zero remainder just before this step is the HCF.

  2. Using the Numbers 15 and 20:

    • Step 1: (20 \div 15 = 1 ) (remainder (5))
      • So, we replace (20) with (15) and (15) with (5).
    • Step 2: (15 \div 5 = 3 ) (remainder (0))
      • When the remainder is (0), the divisor at this step is the HCF.

Thus, the highest common factor of 15 and 20 using the Euclidean algorithm is (5).

Final Answer:

The highest common factor (HCF) of 15 and 20 is 5.