Prime Factorization: Understanding the Process

10 Questions

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

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

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

Using prime factorization

$6$

$3 \times 7$

$63$

Finding the unique prime numbers that can be multiplied together to get a composite number

They can only be divided by 1 and themselves

By identifying common prime factors in the numbers being compared

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.