Divisibility Rules of 17 and 18

Duration: 12 min

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This educational video provides a comprehensive lesson on divisibility rules, focusing on the number 17 and concluding with the rule for 18. The video begins with a title card and a colorful, circular diagram summarizing various divisibility rules. The main content is delivered by an instructor, Yash Jain, who explains three distinct methods for testing divisibility by 17. The first method involves subtracting five times the last digit from the remaining number, with an example demonstrating the process for 3978. The second method, introduced later, is to subtract the last two digits from two times the rest of the number, illustrated with the example 4675. The third method is to add nine times the last digit to five times the rest of the number, with examples including 4675 and 238. The video concludes with the divisibility rule for 18, which states a number is divisible by 18 if it is divisible by both 2 and 9, demonstrated with the number 342. The presentation uses a digital whiteboard for calculations and includes a copyright notice from Knowledge Gate Eduventures.

Chapters

  1. 0:00 – 2:00 00:00-02:00

    The video opens with a title card displaying 'DIVISIBILITY RULES' over a background of scattered numbers. This transitions to a colorful, circular diagram titled 'DIVISIBILITY RULES' which visually summarizes rules for divisibility by 2, 3, 4, 5, 6, 8, 9, 10, and 11. The instructor, Yash Jain, appears in a small window, introducing the topic. The main content begins with a slide titled 'Test for divisibility by 17,' which states the rule: 'Subtract five times the last digit from the remaining leading truncated number. If the result is divisible by 17, then so was the first number. Apply this rule over and over again as necessary.' An example is provided: '3978 --> 397 - 5*8 = 357 --> 35 - 5*7 = 0. So 3978 is divisible by 17.' The instructor begins to explain this rule, and the number 3978 is written on the board.

  2. 2:00 – 5:00 02:00-05:00

    The instructor demonstrates the divisibility test for 17 on the number 3978. He first identifies the last digit as 8 and calculates 5 times 8, which is 40. He then subtracts 40 from the remaining number, 397, to get 357. The process is repeated: the last digit of 357 is 7, and 5 times 7 is 35. Subtracting 35 from 35 gives 0. Since 0 is divisible by 17, the original number 3978 is also divisible by 17. The instructor uses a digital whiteboard to write out each step of the calculation, including the subtraction of 40 from 397 and the subsequent steps, clearly showing the process of reducing the number until a final result is reached.

  3. 5:00 – 10:00 05:00-10:00

    The video introduces a second divisibility rule for 17. The slide is titled 'Divisibility Rule of 17' and states: 'Subtract the last two digits from two times the rest.' An example is given: '4,675: 46 x 2 - 75 = 17.' The instructor demonstrates this with the number 4675. He takes the first part, 46, multiplies it by 2 to get 92, then subtracts the last two digits, 75, to get 17. Since 17 is divisible by 17, the original number is divisible by 17. The instructor then introduces a third rule: 'Add 9 times the last digit to 5 times the rest. Drop trailing zeroes.' Examples are provided: '4,675: 467 x 5 + 5 x 9 = 2380' and '238: 23 x 5 + 8 x 9 = 187.' He begins to work through the first example, calculating 467 x 5 and 5 x 9, and then adding the results.

  4. 10:00 – 12:14 10:00-12:14

    The instructor continues to demonstrate the third divisibility rule for 17. He completes the calculation for 4675, showing that 467 x 5 = 2335 and 5 x 9 = 45, which sum to 2380. He then applies the rule to 238, calculating 23 x 5 = 115 and 8 x 9 = 72, which sum to 187. The video then transitions to the divisibility rule for 18. The slide states: 'It is divisible by 2 and by 9.' An example is given: '342: it is divisible by 2 and by 9.' The instructor demonstrates this by checking if 342 is even (divisible by 2) and then summing its digits: 3 + 4 + 2 = 9, which is divisible by 9. The video concludes with a 'THANKS FOR WATCHING' screen.

The video systematically teaches three different methods for determining if a number is divisible by 17, each offering a unique approach to simplify the problem. The first method uses subtraction, the second uses a combination of multiplication and subtraction, and the third uses addition. This progression demonstrates that complex divisibility rules can be broken down into manageable steps. The lesson concludes with a standard rule for 18, reinforcing the concept that a number can be divisible by a composite number if it is divisible by its prime factors. The clear, step-by-step demonstrations on a digital whiteboard make the abstract rules concrete and easy to follow.