Prime Factors and Greatest Common Factors
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Questions and Answers

The greatest common factor of two numbers is always one of the numbers.

False

What is the greatest common factor of 12 and 15?

3

The multiples of 5 are ___, 10, 15, 20,...

5

How do you find the least common multiple of two numbers?

<p>List the multiples of each number and identify the first multiple that appears in both lists</p> Signup and view all the answers

A factor tree is a diagram that shows the prime factors of a number in a random order.

<p>False</p> Signup and view all the answers

What is the least common multiple of 8 and 12?

<p>24</p> Signup and view all the answers

To create a factor tree, start with the number and divide it by the ___________ prime factor.

<p>smallest</p> Signup and view all the answers

Match the following concepts with their definitions:

<p>Prime Factor = A composite number that divides a given number exactly Greatest Common Factor = The largest number that divides two or more numbers exactly without leaving a remainder Least Common Multiple = The smallest number that is a multiple of two or more numbers Multiples Pattern = The products of a number and the counting numbers</p> Signup and view all the answers

Every positive integer can be expressed as a product of prime factors in a unique way.

<p>True</p> Signup and view all the answers

Study Notes

Prime Factors

  • A prime factor is a prime number that divides a given number exactly without leaving a remainder.
  • Every positive integer can be expressed as a product of prime factors in a unique way, known as the prime factorization.
  • Prime factors are used to simplify fractions, find greatest common factors, and calculate least common multiples.

Greatest Common Factor (GCF)

  • The greatest common factor (GCF) is the largest number that divides two or more numbers exactly without leaving a remainder.
  • To find the GCF, list the prime factors of each number and identify the common prime factors.
  • The GCF is the product of the common prime factors, each raised to the lowest power.

Multiples Patterns

  • Multiples of a number are the products of that number and the counting numbers (1, 2, 3, ...).
  • Multiples patterns can be used to identify relationships between numbers and to solve problems involving multiples.
  • Examples of multiples patterns include:
    • The multiples of 3 are 3, 6, 9, 12, ...
    • The multiples of 4 are 4, 8, 12, 16, ...

Least Common Multiple (LCM)

  • The least common multiple (LCM) is the smallest number that is a multiple of two or more numbers.
  • To find the LCM, list the multiples of each number and identify the first multiple that appears in both lists.
  • The LCM can also be found using prime factorization: list the prime factors of each number, and multiply the highest power of each prime factor that appears in both lists.

Factor Trees

  • A factor tree is a diagram that shows the prime factors of a number.
  • To create a factor tree, start with the number and divide it by the smallest prime factor.
  • Continue dividing each factor by the smallest prime factor until only prime factors remain.
  • The prime factors can be multiplied together to find the original number.

Prime Factors

  • A prime factor is a prime number that divides a given number exactly without leaving a remainder.
  • Every positive integer can be expressed as a product of prime factors in a unique way, known as the prime factorization.
  • Prime factors are used to simplify fractions, find greatest common factors, and calculate least common multiples.

Greatest Common Factor (GCF)

  • The GCF is the largest number that divides two or more numbers exactly without leaving a remainder.
  • To find the GCF, list the prime factors of each number and identify the common prime factors.
  • The GCF is the product of the common prime factors, each raised to the lowest power.

Multiples Patterns

  • Multiples of a number are the products of that number and the counting numbers (1, 2, 3,...).
  • Multiples patterns can be used to identify relationships between numbers and to solve problems involving multiples.
  • Examples of multiples patterns include:
    • The multiples of 3 are 3, 6, 9, 12,...
    • The multiples of 4 are 4, 8, 12, 16,...

Least Common Multiple (LCM)

  • The LCM is the smallest number that is a multiple of two or more numbers.
  • To find the LCM, list the multiples of each number and identify the first multiple that appears in both lists.
  • The LCM can also be found using prime factorization: list the prime factors of each number, and multiply the highest power of each prime factor that appears in both lists.

Factor Trees

  • A factor tree is a diagram that shows the prime factors of a number.
  • To create a factor tree, start with the number and divide it by the smallest prime factor.
  • Continue dividing each factor by the smallest prime factor until only prime factors remain.
  • The prime factors can be multiplied together to find the original number.

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Description

Learn about prime factors, prime factorization, and how they relate to finding the greatest common factor (GCF) of two or more numbers.

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