Divisibility Rules of 2, 3 and 4
Duration: 12 min
This video lesson is available to enrolled students.
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This educational video provides a comprehensive overview of divisibility rules for integers, presented by an instructor in a digital lecture format. The lesson begins with a title slide and a colorful, circular diagram summarizing the rules. The instructor then systematically explains each rule, starting with the fundamental principle that any integer is divisible by 1. This is followed by the rule for divisibility by 2, which states that a number is divisible by 2 if its last digit is even (0, 2, 4, 6, or 8), illustrated with examples like 128 (Yes) and 129 (No). The video then covers the rule for 3, which requires the sum of the digits to be divisible by 3, demonstrated with numbers such as 381 (3+8+1=12, 12÷3=4, Yes) and 217 (2+1+7=10, 10÷3=3 1/3, No). The final rule explained is for 4, which states that a number is divisible by 4 if its last two digits form a number divisible by 4, with examples like 1312 (12÷4=3, Yes) and 7019 (19÷4=4 3/4, No). The video uses on-screen text, handwritten annotations, and a consistent visual style to reinforce the concepts, concluding with a 'Thanks for Watching' screen.
Chapters
0:00 – 2:00 00:00-02:00
The video opens with a title slide displaying 'DIVISIBILITY RULES' over a background of scattered numbers. This transitions to a colorful, hand-drawn circular diagram titled 'DIVISIBILITY RULES' which visually organizes the rules for numbers 2, 3, 4, 5, 6, 9, and 10. The instructor, Yash Jain Sir, appears in a small window in the bottom right corner. The first rule is presented on a slide: '1 Any integer (not a fraction) is divisible by 1'. The instructor explains this fundamental rule, and on-screen text shows examples like 8, 10, 729, and 499, which are all divisible by 1. The instructor uses a digital pen to write '8/1 = 8' and '10/1 = 10' to demonstrate the concept, and a checkmark is added to the rule to confirm its validity.
2:00 – 5:00 02:00-05:00
The video transitions to the second divisibility rule, displayed on a slide with the number '2' in a yellow box. The rule states: 'The last digit is even (0,2,4,6,8)'. The instructor provides examples: '128 Yes' because the last digit is 8, and '129 No' because the last digit is 9. He uses a digital pen to draw a red box around the number 128 and writes 'Yes' with a checkmark, and does the same for 129 with a 'No' and a cross. The instructor then explains the concept of an 'even' number, writing the word 'even' in a circle and drawing an arrow to the list of even digits. He also introduces a mathematical representation, writing 'N = abcabc' and 'N ÷ 2 → R1', to illustrate the concept of divisibility and remainder.
5:00 – 10:00 05:00-10:00
The third divisibility rule is presented on a slide with the number '3' in a yellow box. The rule is: 'The sum of the digits is divisible by 3'. The instructor provides examples: '381 (3+8+1=12, and 12÷3=4) Yes' and '217 (2+1+7=10, and 10÷3=3 1/3) No'. He uses a digital pen to write out the calculations, circling the sum '12' and writing '12÷3=4' with a checkmark. For the second example, he circles '10' and writes '10÷3=3 1/3' with a cross. The slide also includes a note that the rule can be repeated, demonstrated with '99996 (9+9+9+9+6=42, then 4+2=6) Yes'. The instructor writes out the steps for this example, circling '99996', then '42', and finally '6', showing the repeated process to arrive at a single digit.
10:00 – 12:07 10:00-12:07
The fourth divisibility rule is introduced on a slide with the number '4' in a yellow box. The rule states: 'The last 2 digits are divisible by 4'. The instructor provides examples: '1312 is (12÷4=3) Yes' and '7019 is not (19÷4=4 3/4) No'. He uses a digital pen to write the calculations, circling '12' and writing '12÷4=3' with a checkmark, and circling '19' and writing '19÷4=4 3/4' with a cross. The slide also includes a 'quick check' method for small numbers: 'to halve the number twice and the result is still a whole number'. Examples are given: '12/2=6, 6/2=3, 3 is a whole number. Yes' and '30/2=15, 15/2=7.5 which is not a whole number. No'. The instructor demonstrates this with the number 1214, writing '1214 ÷ 2 = 607' and '607 ÷ 2 = 303.5', concluding it is not divisible by 4. The video concludes with a 'THANKS FOR WATCHING' screen.
The video presents a clear, structured, and progressive lesson on divisibility rules. It begins with the most fundamental rule (divisibility by 1) and systematically builds upon it, introducing rules for 2, 3, and 4. The teaching method is highly visual, using a combination of on-screen text, a hand-drawn diagram, and real-time digital annotations to explain each concept. The instructor reinforces each rule with multiple worked examples, clearly labeling them as 'Yes' or 'No' and using checkmarks and crosses to indicate correctness. The progression from simple rules (like checking the last digit) to more complex ones (like summing digits) is logical and effective for student understanding. The inclusion of a 'quick check' for divisibility by 4 adds a practical shortcut, demonstrating a well-organized and pedagogically sound approach to teaching this mathematical topic.