Divisibility rules for 3, 4, 6, 8 and 9

Math Mammoth
18 Jul 201611:27
EducationalLearning
32 Likes 10 Comments

TLDRThe video script by Maria Miller introduces various divisibility rules and tests, explaining how to determine if a number is divisible by integers such as 2, 3, 4, 5, 6, 8, 9, and 10. It covers basic rules like even numbers and ends-in rules for 5 and 10, as well as sum of digits methods for 3, 4, and 9. The script also explains the process of checking divisibility for numbers by applying these rules, offering a comprehensive guide to understanding and applying divisibility tests.

Takeaways
  • 📐 A number is divisible by 2 if it is an even number, ending in 0, 2, 4, 6, or 8.
  • 🐝 A number is divisible by 5 if it ends in 0 or 5, following the skip counting pattern.
  • 🔢 Divisibility by 10 can be determined if the number ends in 0, as with 40, 60, 100, or 1000.
  • 💱 For divisibility by 100, check if the number ends in two zeros, such as in 200, 300, etc.
  • 🔍 A number is divisible by 3 if the sum of its digits is divisible by 3, demonstrated with examples like 358 (3+5+8=16).
  • 🔢 Divisibility by 9 is similar to divisibility by 3, but checking if the sum of digits is divisible by 9, e.g., 1+2+8+5+3=19.
  • 📂 A number is divisible by 4 if the number formed from its last two digits is divisible by 4, as seen with 124 (last two digits 24).
  • ⚖️ Divisibility by 6 is confirmed if the number is even and the sum of its digits is divisible by 3, using the rules for 2 and 3.
  • 📐 Divisibility by 8 can be checked by taking half of the number and seeing if it is divisible by 4.
  • 🔢 The divisibility rule for 7 and 11 is more complex and not covered in the script, suggesting the use of long division for these cases.
  • 📊 The script provides a comprehensive overview of divisibility rules for numbers 2 through 10, with exceptions for 7 and 11.
Q & A
  • What is the basic rule for determining if a number is divisible by 2?

    -A number is divisible by 2 if it is an even number, meaning it ends in 0, 2, 4, 6, or 8.

  • How can you quickly check if a number is divisible by 5?

    -If a number ends in 0 or 5, it is divisible by 5.

  • What is the rule for divisibility by 10?

    -A number is divisible by 10 if it ends in 0, such as 40, 60, 100, 1000, etc.

  • How can you determine if a number is divisible by 3?

    -A number is divisible by 3 if the sum of its digits is divisible by 3.

  • What is the logic behind checking if a number is divisible by 9?

    -A number is divisible by 9 if the sum of its digits is divisible by 9.

  • What rule is used to determine divisibility by 4?

    -A number is divisible by 4 if the number formed from its last two digits is divisible by 4.

  • How does divisibility by 6 relate to divisibility by 2 and 3?

    -A number is divisible by 6 if it is an even number and also divisible by 3.

  • What is the basic rule for divisibility by 8?

    -A number is divisible by 8 if taking half of it (rounding up if necessary) results in a number that is divisible by 4.

  • Why are there no simple divisibility rules for numbers like 7, 72, and 11?

    -There are no simple divisibility rules for numbers like 7, 72, and 11 because they do not follow the same patterns as other numbers, thus requiring more complex methods like long division for verification.

  • How can you use the divisibility rules to quickly determine if a number is divisible by several numbers at once?

    -You can apply each divisibility rule in sequence to quickly narrow down which numbers a given number is divisible by, using the rules for 2, 3, 4, 5, 6, 8, 9, and 10 as a checklist.

  • What is the significance of the skip counting pattern in learning divisibility?

    -The skip counting pattern helps in understanding the regular intervals at which multiples of a number occur, aiding in recognizing divisibility rules and their application.

  • How can you verify the divisibility of a number using long division?

    -Long division can be used to check if a number is divisible by another by dividing the dividend by the divisor and checking for a remainder. If there is no remainder, the number is divisible.

Outlines
00:00
📚 Introduction to Divisibility Rules

This paragraph introduces the concept of divisibility rules, also known as divisibility tests. Maria Miller begins by explaining the basic rules for determining if a number is divisible by 2, 3, 4, 5, and 10. She mentions that even numbers ending in 0, 2, 4, 6, or 8 are divisible by 2, and numbers ending in 0 or 5 are divisible by 5. For divisibility by 3, she introduces a rule that involves summing the digits of the number and checking if the sum is divisible by 3. Similarly, for divisibility by 9, the sum of the digits must be divisible by 9. The paragraph also covers the rule for a number to be divisible by 4, which is to check if the last two digits form a number divisible by 4. The explanation includes examples to illustrate these rules and emphasizes their simplicity and practicality in everyday calculations.

05:03
🔢 Applying Divisibility Rules to Numbers

In this paragraph, Maria Miller demonstrates how to apply the divisibility rules to various numbers. She explains the process of checking if a number is divisible by 6, which requires the number to be even and divisible by 3. The paragraph delves into the divisibility rule for 8, stating that a number is divisible by 8 if half of the number is divisible by 4. Maria also addresses the complexity of divisibility rules for 7 and 11, acknowledging that they are more complicated and that long division is used to check divisibility by these numbers. The summary includes a step-by-step application of the rules to specific numbers, highlighting the process of elimination and verification through long division where necessary.

10:06
📈 Comprehensive Divisibility Check and Conclusion

The final paragraph presents a comprehensive check for divisibility of numbers by a range of divisors from 2 to 10. Maria Miller walks through the process of determining if a number is divisible by each of these divisors, using both the established divisibility rules and long division for more complex cases like 7. The paragraph emphasizes the importance of following the rules in order and using long division as a fallback when necessary. The summary concludes with a brief overview of the divisibility rules covered in the video and their utility in mathematical problem-solving, reinforcing the educational value of the content.

Mindmap
Keywords
💡Divisibility Rules
Divisibility rules are mathematical principles that help determine whether a number can be evenly divided by another number without leaving a remainder. In the video, these rules are essential for understanding how to quickly identify if a number is divisible by certain integers, such as 2, 3, 4, 5, 6, 8, 9, and 10. The rules are applied to various examples throughout the video to demonstrate how they can be used to simplify the process of division and mental calculation.
💡Even Numbers
Even numbers are integers that can be divided by 2 without leaving a remainder. In the context of the video, determining if a number is even is the first step in applying several divisibility rules, as it helps to quickly identify potential divisibility by other numbers such as 4, 6, and 10. The video uses evenness as a criterion for divisibility by 2 and, subsequently, by multiples of 2 like 4, 6, and 10.
💡Digit Sum
The digit sum of a number is the result of adding up all its individual digits. This concept is crucial in the video when applying divisibility tests for numbers like 3 and 9, where the divisibility of a number is determined by whether the sum of its digits is divisible by 3 or 9, respectively. The digit sum is a quick mental calculation tool used to assess divisibility without the need for long division.
💡Divisibility Test
A divisibility test is a method used to determine whether one integer can be divided by another without leaving a remainder. The video focuses on various divisibility tests for different numbers, providing specific rules and patterns to recognize divisibility. These tests are fundamental for simplifying the process of division and are used to check divisibility by numbers like 2, 3, 4, 5, 6, 8, 9, and 10.
💡Divisible by 4
A number is divisible by 4 if the number formed by its last two digits is divisible by 4. This rule is derived from the fact that 100 is divisible by 4, and any number that is a multiple of 100 plus a multiple of 4 will also be divisible by 4. In the video, this rule is used to quickly determine the divisibility of numbers like 124 and 8080 by focusing on the last two digits.
💡Divisible by 6
A number is divisible by 6 if it is both an even number and divisible by 3. This is because 6 is the least common multiple of 2 and 3, meaning that for a number to be divisible by 6, it must satisfy both the conditions of being even (divisible by 2) and having a digit sum divisible by 3. The video uses this rule to explain how to check if a number can be evenly divided by 6.
💡Divisible by 8
A number is divisible by 8 if taking half of it (or dividing it by 2 repeatedly until the result is a single digit) results in a number that is divisible by 4. This rule is based on the fact that 8 is a power of 2, and by successively halving the number, one can reduce the problem to checking the divisibility by 4 of a single digit. The video uses this rule to explain how to quickly determine if a number is divisible by 8.
💡Divisibility by 10
A number is divisible by 10 if it ends in 0. This is because 10 is a base unit of our number system, and any multiple of 10 will have a zero in the ones place. In the video, this rule is used as a simple check for divisibility by 10, as it only requires looking at the last digit of the number.
💡Long Division
Long division is a method of dividing one integer by another and finding the quotient and remainder, if any. In the video, long division is mentioned as a more traditional and less efficient way to check divisibility, especially for numbers that do not have straightforward divisibility rules like 7. It involves breaking down the division process into simpler steps to arrive at the result.
💡Divisibility by 3
A number is divisible by 3 if the sum of its digits is divisible by 3. This rule is based on the property that the sum of the digits of multiples of 3 will also be a multiple of 3. In the video, this rule is applied to various numbers to demonstrate how to quickly determine if they can be evenly divided by 3 without performing the actual division.
💡Divisibility by 9
A number is divisible by 9 if the sum of its digits is divisible by 9. This divisibility rule is similar to the one for 3 but uses the number 9 instead. It is based on the property that the digit sum of multiples of 9 will also be a multiple of 9. The video uses this rule to explain how to check if a number can be divided by 9 without performing the actual division.
Highlights

Maria Miller introduces divisibility rules and tests, providing a foundational understanding of number divisibility.

A number is divisible by 2 if it is an even number, ending in 0, 2, 4, 6, or 8.

Divisibility by 5 is determined if a number ends in 0 or 5, following the skip counting pattern.

Numbers ending in 0 are divisible by 10, and the pattern extends to larger multiples such as 100 and 1000.

Divisibility by 3 is identified by checking if the sum of a number's digits is divisible by 3.

For divisibility by 9, the same principle of digit sum divisibility applies.

Divisibility by 4 is determined by checking if the number formed from its last two digits is divisible by 4.

Numbers divisible by 6 must be even and also divisible by 3, applying both divisibility rules.

Divisibility by 8 is checked by seeing if half of the number is divisible by 4.

The video explains that every number has a divisibility rule except for 7 and 11, which require more complex methods.

Long division is suggested for checking divisibility by 7, as the rule is not as straightforward.

The video demonstrates the divisibility tests using various examples, making the concepts clear through practical application.

Maria Miller's explanation emphasizes the importance of understanding divisibility rules for problem-solving in mathematics.

The video is educational, providing a comprehensive overview of divisibility rules that can be applied in various mathematical contexts.

The method for checking divisibility by 3 and 9 is highlighted by showing how digit sums relate to these rules.

The video simplifies complex mathematical concepts, making them accessible for learners at different levels.

Maria Miller's approach to teaching divisibility rules is systematic and easy to follow, enhancing the learning experience.

The video serves as a valuable resource for those looking to improve their understanding of number properties and divisibility.

Transcripts
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