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Questions and Answers
What is the condition for a number to be divisible by 3?
What is the condition for a number to be divisible by 3?
What is the condition for a number to be divisible by 9?
What is the condition for a number to be divisible by 9?
What is the condition for a number to be divisible by 6?
What is the condition for a number to be divisible by 6?
If a number is divisible by 3 and 2, what else can be concluded?
If a number is divisible by 3 and 2, what else can be concluded?
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What is a common real-world application of divisibility rules?
What is a common real-world application of divisibility rules?
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If a number is divisible by 9, what else can be concluded?
If a number is divisible by 9, what else can be concluded?
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What is the purpose of using divisibility rules?
What is the purpose of using divisibility rules?
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Study Notes
Divisibility Rules
Divisibility By 3 With Sum Of Digits
- A number is divisible by 3 if the sum of its digits is also divisible by 3.
- Example: 123 is divisible by 3 because 1 + 2 + 3 = 6, which is divisible by 3.
Divisibility By 6 With Even Number And Sum Of Digits
- A number is divisible by 6 if it is even (last digit is 0, 2, 4, 6, or 8) and the sum of its digits is divisible by 3.
- Example: 120 is divisible by 6 because it is even (last digit is 0) and 1 + 2 + 0 = 3, which is divisible by 3.
Divisibility By 9 With Sum Of Digits And Remainder
- A number is divisible by 9 if the sum of its digits is divisible by 9 or if the remainder when divided by 9 is 0.
- Example: 459 is divisible by 9 because 4 + 5 + 9 = 18, which is divisible by 9.
Relationship Between Divisibility Rules
- If a number is divisible by 3 and 2, it is also divisible by 6.
- If a number is divisible by 9, it is also divisible by 3.
Applying Divisibility Rules To Real-world Problems
- Divisibility rules can be used to quickly check if a number is divisible by a certain number without having to perform the actual division.
- Examples: checking if a number is divisible by 3 or 6 when splitting a group of people into teams, or checking if a number is divisible by 9 when calculating the total cost of items.
Prime Factors
- A prime factor is a prime number that divides a given number exactly without leaving a remainder.
- Example: the prime factors of 12 are 2, 2, and 3 because 2 × 2 × 3 = 12.
- Prime factors are used to find the greatest common divisor (GCD) and least common multiple (LCM) of two or more numbers.
Divisibility Rules
Divisibility by 3
- A number is divisible by 3 if the sum of its digits is also divisible by 3.
- This rule can be applied to any number, regardless of its size.
Divisibility by 6
- A number is divisible by 6 if it is even (last digit is 0, 2, 4, 6, or 8) and the sum of its digits is divisible by 3.
- This rule combines two conditions: even number and sum of digits being divisible by 3.
Divisibility by 9
- A number is divisible by 9 if the sum of its digits is divisible by 9 or if the remainder when divided by 9 is 0.
- This rule provides two alternative ways to check for divisibility by 9.
Relationships Between Divisibility Rules
- If a number is divisible by 3 and 2, it is also divisible by 6.
- If a number is divisible by 9, it is also divisible by 3.
- These relationships can be used to simplify divisibility checks.
Applications of Divisibility Rules
- Divisibility rules can be used to quickly check if a number is divisible by a certain number without performing actual division.
- Examples include checking divisibility by 3 or 6 when splitting a group into teams, or checking divisibility by 9 when calculating the total cost of items.
Prime Factors
- A prime factor is a prime number that divides a given number exactly without leaving a remainder.
- Prime factors are used to find the greatest common divisor (GCD) and least common multiple (LCM) of two or more numbers.
- Example: the prime factors of 12 are 2, 2, and 3, as 2 × 2 × 3 = 12.
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Description
Learn the rules to determine if a number is divisible by 3 and 6. Test your understanding of these essential math concepts.
