Divisibility Rules of 5, 6 and 7

Duration: 12 min

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This educational video provides a comprehensive tutorial on divisibility rules, presented by an instructor in a picture-in-picture format. The lesson begins with an introduction to the topic, followed by a detailed explanation of the rule for divisibility by 5, which states that a number is divisible by 5 if its last digit is 0 or 5. The instructor demonstrates this rule with examples, such as 175 (Yes) and 809 (No), and then transitions to a more advanced method for checking divisibility by 5 using a formula: N = a x b, where a is the number formed by removing the last digit and b is the last digit. The video then moves to the rule for divisibility by 6, which requires a number to be both even and divisible by 3. This is illustrated with examples like 114 (Yes) and 308 (No). The final segment of the video introduces a 'trick' for divisibility by 7, which involves a specific calculation: multiplying the last digit by 2 and adding it to the remaining number, then checking if the result is divisible by 7. This method is demonstrated with the number 672, where 67 + (2 x 2) = 71, and then 7 + (1 x 2) = 9, which is not divisible by 7, so 672 is not divisible by 7. The video concludes with a 'Thanks for Watching' screen.

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. It then transitions to a colorful, hand-drawn circular diagram titled 'DIVISIBILITY RULES' that outlines various rules. The instructor, Yash Jain Sir, appears in a small window in the bottom right corner. The first rule presented is for divisibility by 5, with the on-screen text stating, 'The last digit is 0 or 5'. Two examples are given: 175 is marked as 'Yes' because its last digit is 5, and 809 is marked as 'No' because its last digit is 9. The instructor begins to explain the rule, and the on-screen text 'The last digit is 0 or 5' is highlighted.

  2. 2:00 – 5:00 02:00-05:00

    The instructor continues to explain the divisibility rule for 5. He writes the formula 'N = a x b' on the screen, where N is the number, a is the number formed by removing the last digit, and b is the last digit. He demonstrates this with the number 175, writing '17' for a and '5' for b, and then shows that 17 x 5 = 85. He then explains that if the product is divisible by 5, the original number is divisible by 5. He uses the example of 809, writing '80' for a and '9' for b, and shows that 80 x 9 = 720, which is divisible by 5, but since the last digit is 9, the number 809 is not divisible by 5. The instructor emphasizes that the rule is based on the last digit being 0 or 5, not the product.

  3. 5:00 – 10:00 05:00-10:00

    The video transitions to the divisibility rule for 6. The on-screen text states, 'Is even and is divisible by 3 (it passes both the 2 rule and 3 rule above)'. The instructor explains that a number must be even and the sum of its digits must be divisible by 3. He provides the example of 114, noting it is even and the sum of its digits (1+1+4=6) is divisible by 3, so 114 is divisible by 6. He then shows the example of 308, which is even but the sum of its digits (3+0+8=11) is not divisible by 3, so 308 is not divisible by 6. The instructor then introduces a 'trick' for divisibility by 7, writing the number 672 on the screen and explaining the method: multiply the last digit by 2 and add it to the remaining number. He demonstrates this with 672, showing 67 + (2 x 2) = 71.

  4. 10:00 – 12:29 10:00-12:29

    The instructor continues the 'trick' for divisibility by 7. He takes the result from the previous step, 71, and applies the same rule: 7 + (1 x 2) = 9. Since 9 is not divisible by 7, the original number 672 is not divisible by 7. He then demonstrates the method with another number, 105. He writes 105, multiplies the last digit (5) by 2 to get 10, and adds it to the remaining number (10), resulting in 20. He then applies the rule again to 20: 2 + (0 x 2) = 2, which is not divisible by 7, so 105 is not divisible by 7. He repeats the process with 905, showing that 90 + (5 x 2) = 100, and then 10 + (0 x 2) = 10, which is not divisible by 7. The video ends with a 'Thanks for Watching' screen.

The video presents a structured and progressive lesson on divisibility rules, starting with the fundamental rule for 5 and moving to more complex rules for 6 and 7. The instructor uses a combination of on-screen text, hand-drawn diagrams, and worked examples to clearly explain each concept. The lesson is designed to be accessible, with a focus on practical application and a 'trick' for divisibility by 7 that simplifies the process. The overall teaching style is engaging and methodical, making the content easy to follow and understand.