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Prime Factorization: Understanding the Process

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Prime Factorization: Understanding the Process

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Questions and Answers

What is prime factorization?

The process of obtaining the unique prime numbers that multiply into a larger number (correct)

The process of subtracting prime numbers to obtain a larger number

The process of obtaining any numbers that multiply into a larger number

The process of adding prime numbers to obtain a larger number

What is a composite number?

A negative whole number that is prime and cannot be divided into smaller whole numbers

A positive whole number that is not prime and can be divided into smaller whole numbers (correct)

A positive whole number that is prime and cannot be divided into smaller whole numbers

A negative whole number that is not prime and can be divided into smaller whole numbers

How do prime factors relate to prime numbers?

Prime factors are the result of adding two prime numbers together

Prime factors are any set of numbers that can be multiplied to create a larger number

Prime factors are the prime numbers that can be multiplied to create a larger number (correct)

Prime factors are the result of subtracting two prime numbers from each other

What method can be used to find the LCM of any two numbers?

Using prime factorization Signup and view all the answers

What is the LCM of 2 and 3?

$6$ Signup and view all the answers

What is the prime factorization of 21?

$3 \times 7$ Signup and view all the answers

What is the least common multiple of 21 and 9?

$63$ Signup and view all the answers

What is prime factorization?

Finding the unique prime numbers that can be multiplied together to get a composite number Signup and view all the answers

What are prime factors special for?

They can only be divided by 1 and themselves Signup and view all the answers

How can prime factors be used for finding greatest common factors (GCF) and least common multiples (LCM)?

By identifying common prime factors in the numbers being compared Signup and view all the answers

Study Notes

Prime factorization is the process of finding the unique prime numbers that can be multiplied together to get a composite number.
Prime factors are special because they can only be divided by 1 and themselves.
To find prime factors, multiply together the identified prime numbers until the result matches the original number.
The prime numbers under 30 are commonly used in prime factorization.
Serial factorization method involves factoring out the smallest prime number repeatedly until the remaining factors are prime.
Prime factors can be organized in a table (tee chart) for easy reference during serial factorization.
Factor tree method involves breaking down the number into factors and continuing the process with each resulting factor until prime factors are reached.
Prime factorization is used for various purposes, including finding greatest common factors (GCF) and least common multiples (LCM).
Greatest common factors are the largest numbers that can divide two numbers evenly, and can be found by identifying common prime factors.
Least common multiples are the smallest numbers that two numbers can be multiplied into, and can also be found by identifying common prime factors.

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Description

Learn about prime factorization, the process of obtaining the unique prime numbers that multiply into a larger number. Discover how to break down this topic into manageable steps and explore multiple methods for finding a number's prime factorization.