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Questions and Answers
What can be inferred if 45 is a multiple of 9?
What can be inferred if 45 is a multiple of 9?
What is the first non-zero multiple of 6?
What is the first non-zero multiple of 6?
Why are there infinite multiples of any integer?
Why are there infinite multiples of any integer?
What is the smallest multiple of 8 that is greater than or equal to 8?
What is the smallest multiple of 8 that is greater than or equal to 8?
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Which statement correctly describes every integer's relationship with the number 1?
Which statement correctly describes every integer's relationship with the number 1?
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What is the first non-zero multiple of 5?
What is the first non-zero multiple of 5?
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In a time-driven scheduling system where tasks execute every 12 seconds, when will the first four executions occur?
In a time-driven scheduling system where tasks execute every 12 seconds, when will the first four executions occur?
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If a data logger records data every 3 minutes, which times represent the first five recordings?
If a data logger records data every 3 minutes, which times represent the first five recordings?
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Which of the following statements correctly describes a factor?
Which of the following statements correctly describes a factor?
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In regards to multiples, which statement is true?
In regards to multiples, which statement is true?
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Study Notes
Properties of Multiples
- An infinite number of multiples exists for any integer due to continual multiplication by increasing integers.
- Multiples of a number are always greater than or equal to that number, with 0 being a special multiple of any integer.
- Every number is a multiple of 1, as any number multiplied by 1 yields the number itself.
- If B is a multiple of A, then A is a factor of B, demonstrating the interrelation of factors and multiples.
Examples and Practice Questions
- The first non-zero multiple of 7 is 7.
- If 36 is a multiple of 6, it implies that 6 is a factor of 36.
- The smallest multiple of 8 that is greater than or equal to 8 is 8.
- Multiples of 5 are infinite because you can multiply it by any integer to yield unique products.
Applications of Multiples
- Time-driven scheduling systems use multiples for periodic tasks, such as executing a task every 3 seconds, resulting in activities at 3, 6, 9 seconds, etc.
- Email applications might check for new messages every 15 minutes, running tasks at intervals like 15, 30, and 45 minutes.
- Data collection in a sensor network can occur every 5 minutes, resulting in actions at 5, 10, 15 minutes, and so on.
First Non-zero Multiples
- The first four multiples of 7 are 7, 14, 21, and 28.
- The first six multiples of 4 are 4, 8, 12, 16, 20, and 24.
- The first five multiples of 9 are 9, 18, 27, 36, and 45.
Multiples of an Integer
- A multiple of an integer n is expressed as n × k, where k is an integer.
- Examples include multiples of 5: 5, 10, 15, 20, etc., and multiples of 8: 8, 16, 24, 32, etc.
Properties of Factors
- Factors of a number are always less than or equal to that number.
- Every number has at least two factors: 1 and the number itself.
- Understanding factors is essential for divisibility and simplifying complex problems.
Practice with Factors
- Possible factors of 18 include 2; 20, 19, and 25 are not factors.
- Factors are always less than or equal to the number, unlike other types of numbers.
- Factors of 12 include 1, 3, 12, but 15 cannot be a factor.
Finding Multiples
- To find multiples of a number n, start from 1 and check for divisibility with decreasing integers.
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Description
Explore the concept of multiples with this quiz that delves into the infinite nature of multiples for any integer. Understand why every number is a multiple of 1 and the special case of zero as a multiple. Test your knowledge and comprehension of these fundamental mathematical principles.
