Podcast
Questions and Answers
What is the prime factorization of the number 60?
What is the prime factorization of the number 60?
Which method can be used to find common factors of two numbers?
Which method can be used to find common factors of two numbers?
If the common factors of 12 and 18 are 1, 2, 3, and 6, what is the greatest common factor (GCF)?
If the common factors of 12 and 18 are 1, 2, 3, and 6, what is the greatest common factor (GCF)?
What does the Fundamental Theorem of Arithmetic state regarding prime factorization?
What does the Fundamental Theorem of Arithmetic state regarding prime factorization?
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Which of the following is NOT a step in the prime factorization method?
Which of the following is NOT a step in the prime factorization method?
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Study Notes
Factorization
Prime Factorization
- Definition: The process of expressing a number as the product of its prime numbers.
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Method:
- Start with the number.
- Divide by the smallest prime number (2, 3, 5, etc.).
- Continue dividing until all factors are prime.
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Example:
- For 60:
60 = 2 × 30
30 = 2 × 15
15 = 3 × 5
Final result: 60 = 2² × 3¹ × 5¹.
- For 60:
- Importance: Prime factorization is unique for every integer (Fundamental Theorem of Arithmetic).
Common Factors
- Definition: A common factor of two or more numbers is a number that divides each of them without leaving a remainder.
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Finding Common Factors:
- List all factors of each number.
- Identify which factors appear in each list.
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Methods:
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Prime Factorization Method:
- Perform prime factorization for each number.
- Identify the lowest power of common primes.
- Listing Method: List factors of each number and find overlaps.
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Prime Factorization Method:
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Example:
- For numbers 12 and 18:
- Factors of 12: 1, 2, 3, 4, 6, 12
- Factors of 18: 1, 2, 3, 6, 9, 18
- Common Factors: 1, 2, 3, 6
- Greatest Common Factor (GCF): 6.
- For numbers 12 and 18:
- Use in Simplification: Knowing common factors helps in simplifying fractions and finding GCF.
Prime Factorization
- Expressing a number as a product of prime numbers
- Start by dividing the number by the smallest prime number
- Continue dividing until all factors are prime
- 60 can be expressed as 2² × 3¹ × 5¹
- Prime factorization is unique for every integer (Fundamental Theorem of Arithmetic)
Common Factors
- A factor that divides two or more numbers without leaving a remainder
- Find common factors by listing all factors of each number and identifying overlaps
- Prime Factorization Method: Perform prime factorization for each number and identify the lowest power of common primes
- For 12 and 18:
- Factors of 12: 1, 2, 3, 4, 6, 12
- Factors of 18: 1, 2, 3, 6, 9, 18
- Common Factors: 1, 2, 3, 6
- Greatest Common Factor (GCF): 6
- Understanding common factors helps in simplifying fractions and finding the GCF
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Description
This quiz covers important concepts related to factorization, including prime factorization and common factors. It aims to provide a clear understanding of how to express numbers as products of their prime factors and identify common factors among given numbers. Master these essential skills to enhance your mathematical proficiency.
