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Questions and Answers
What is a prime factor?
What is a prime factor?
What is the correct way to find the prime factors of a number?
What is the correct way to find the prime factors of a number?
What is true about the prime factors of a composite number?
What is true about the prime factors of a composite number?
What is the importance of prime factors in mathematics?
What is the importance of prime factors in mathematics?
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What are the prime factors of 24?
What are the prime factors of 24?
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What is a factor of a number?
What is a factor of a number?
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A number can have only one factor.
A number can have only one factor.
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What is a multiple of a number?
What is a multiple of a number?
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The factors of a number are always _______________ or equal to the number.
The factors of a number are always _______________ or equal to the number.
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What is an example of a real-world application of factors and multiples?
What is an example of a real-world application of factors and multiples?
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If a is a multiple of b, then b is a factor of a.
If a is a multiple of b, then b is a factor of a.
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How can you find the factors of a number?
How can you find the factors of a number?
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Match the following terms with their definitions:
Match the following terms with their definitions:
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Study Notes
Prime Factors
Definition: A prime factor is a prime number that divides a given number exactly without leaving a remainder.
Key Properties:
- Prime factors are always prime numbers.
- A prime factor can be divided only by 1 and itself.
- Every composite number can be expressed as a product of prime factors in a unique way, except for the order in which they are listed.
Examples:
- The prime factors of 12 are: 2, 2, 3 (since 2 × 2 × 3 = 12)
- The prime factors of 24 are: 2, 2, 2, 3 (since 2 × 2 × 2 × 3 = 24)
- The prime factors of 36 are: 2, 2, 3, 3 (since 2 × 2 × 3 × 3 = 36)
Finding Prime Factors:
- Divide the number by the smallest prime number (2) as long as it's divisible.
- Then, divide by the next prime number (3) as long as it's divisible.
- Continue this process until the number is reduced to 1.
- The prime factors are the prime numbers that were used to divide the original number.
Importance:
- Prime factors are essential in number theory and are used in various mathematical concepts, such as fractions, decimals, and percentages.
- They are also used in cryptography and coding theory.
- Understanding prime factors is crucial for solving problems involving divisibility, greatest common divisors (GCDs), and least common multiples (LCMs).
Prime Factors
- A prime factor is a prime number that divides a given number exactly without leaving a remainder.
Key Properties
- Prime factors are always prime numbers.
- A prime factor can be divided only by 1 and itself.
- Every composite number can be expressed as a product of prime factors in a unique way, except for the order in which they are listed.
Examples of Prime Factors
- The prime factors of 12 are 2, 2, 3, since 2 × 2 × 3 = 12.
- The prime factors of 24 are 2, 2, 2, 3, since 2 × 2 × 2 × 3 = 24.
- The prime factors of 36 are 2, 2, 3, 3, since 2 × 2 × 3 × 3 = 36.
Finding Prime Factors
- Divide the number by the smallest prime number (2) as long as it's divisible.
- Then, divide by the next prime number (3) as long as it's divisible.
- Continue this process until the number is reduced to 1.
- The prime factors are the prime numbers that were used to divide the original number.
Importance of Prime Factors
- Prime factors are essential in number theory and are used in various mathematical concepts, such as fractions, decimals, and percentages.
- They are also used in cryptography and coding theory.
- Understanding prime factors is crucial for solving problems involving divisibility, greatest common divisors (GCDs), and least common multiples (LCMs).
Factors
- A factor is a whole number that divides another number exactly without leaving a remainder.
- Factors of a number are the numbers that multiply together to give that number.
- Example: factors of 12 are 1, 2, 3, 4, 6, and 12.
Types of Factors
- Prime factors: prime numbers that divide a number exactly without leaving a remainder.
- Composite factors: non-prime numbers that divide a number exactly without leaving a remainder.
Multiples
- A multiple is a product of a number and an integer.
- Example: multiples of 3 are 3, 6, 9, 12,...
- A number can have infinite multiples.
Finding Factors and Multiples
- To find factors of a number, list all numbers that divide it exactly without leaving a remainder.
- To find multiples of a number, multiply it by a series of integers (1, 2, 3,...).
Properties of Factors and Multiples
- Factors of a number are always less than or equal to the number.
- Multiples of a number are always greater than or equal to the number.
- If a is a factor of b, then b is a multiple of a.
- If a is a multiple of b, then b is a factor of a.
Real-World Applications
- Factors and multiples are used in everyday life, such as:
- Measuring lengths and quantities
- Calculating areas and volumes
- Solving problems involving ratios and proportions
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Description
Understand the definition and key properties of prime factors, and learn how to express composite numbers as a product of prime factors. Test your knowledge with examples and more!
