Short Trick to find HCF by minimum difference method

Duration: 14 min

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This educational video, presented by Yash Jain from Knowledge Gate, provides a detailed tutorial on finding the Highest Common Factor (HCF) using the Minimum Difference Method. The video begins with an introduction to the topic, followed by a step-by-step demonstration of the method. The core of the lesson involves calculating the HCF of two numbers by repeatedly subtracting the smaller from the larger, then using the resulting difference and the smaller number for the next iteration. This process is shown to be equivalent to the Euclidean algorithm. The instructor applies this method to several examples, including HCF(56, 84), HCF(15, 39, 153), and HCF(238, 322, 434), illustrating how to handle both two and three numbers. The video emphasizes that the minimum difference obtained is not always the final HCF, as it may need to be factored further. The lesson concludes with a final example, HCF(5, 18), which results in an HCF of 1, reinforcing the concept that if all factors are eliminated, the HCF is 1.

Chapters

  1. 0:00 – 2:00 00:00-02:00

    The video opens with a title card displaying "LCM & HCF" against a digital background. It then transitions to a presentation slide with a cartoon teacher and the text "HCF" and "LCM". The instructor, Yash Jain, introduces the topic of HCF and begins to explain the Minimum Difference Method. The on-screen text clearly states "4. HCF by Minimum Difference Method" and presents the first example: "HCF (56, 84)". The instructor explains that the minimum difference will not be the final answer and that some factors may be eliminated.

  2. 2:00 – 5:00 02:00-05:00

    The instructor demonstrates the Minimum Difference Method for HCF(56, 84). He first calculates the difference: 84 - 56 = 28. He then factors 28 as 2 x 2 x 7. The next step is to divide both original numbers by 28, resulting in 56/28 = 2 and 84/28 = 3. The process continues by finding the HCF of the new numbers, 2 and 3. The instructor writes the numbers 2 and 3 in a box and states that the HCF of 2 and 3 is 1, which is a key point in the method.

  3. 5:00 – 10:00 05:00-10:00

    The instructor continues the example of HCF(56, 84). He shows that the HCF of 2 and 3 is 1, which means the HCF of the original numbers is 28. He then moves to the next example, HCF(15, 39, 153). He calculates the minimum difference between the numbers: 39 - 15 = 24, 153 - 39 = 114, and 153 - 15 = 138. The minimum difference is 24. He factors 24 as 2 x 2 x 2 x 3. He then divides each of the original numbers by 24, but since 15 is not divisible by 24, he proceeds to the next step, which is to find the HCF of the new set of numbers.

  4. 10:00 – 13:33 10:00-13:33

    The instructor continues with the example HCF(15, 39, 153). He divides the numbers by the minimum difference, 24, and gets 15/24, 39/24, and 153/24. He then finds the HCF of the new numbers, which are 15, 39, and 153. He calculates the minimum difference again, which is 24, and factors it as 2 x 2 x 2 x 3. He then divides the numbers by 24, but since 15 is not divisible by 24, he proceeds to the next step. He then moves to the next example, HCF(238, 322, 434). He calculates the minimum difference, which is 84, and factors it as 2 x 2 x 3 x 7. He then divides the numbers by 84, but since 238 is not divisible by 84, he proceeds to the next step. He then moves to the final example, HCF(5, 18). He calculates the minimum difference, which is 13, and factors it as 13. He then divides the numbers by 13, but since 5 is not divisible by 13, he proceeds to the next step. He then concludes that the HCF of 5 and 18 is 1.

The video provides a comprehensive and structured lesson on the Minimum Difference Method for finding the Highest Common Factor. It begins by introducing the method and its core principle: repeatedly finding the minimum difference between numbers and using it to simplify the problem. The instructor uses a clear, step-by-step approach, demonstrating the method on multiple examples of increasing complexity, from two numbers to three numbers. A key insight emphasized throughout is that the minimum difference is a starting point, not the final answer, and must be factored and used in subsequent iterations. The lesson effectively connects this method to the fundamental concept of the Euclidean algorithm, showing how subtraction is used to find the HCF. The progression from simple examples to more complex ones, culminating in the case where the HCF is 1, provides a complete understanding of the technique.