# Factorization, GCD, LCM

The printable prime factorization worksheets on this page require students to factor progressively larger integers into their prime factors. This is the first step for determining the greatest common divisors of two numbers, or determining the least common multiple of two numbers, but additionally prime factorization introduces the concepts of prime numbers and composite numbers.

## Prime Factorization

These worksheets require trees to determine the prime factorization of a number, including showing expanded and exponential forms.

## Prime Factorization Worksheets

All numbers are made up of prime factors, and the list of primes whose product is a particular number are called that number's prime factorization. The prime factorization worksheets in this section require students to take a number and break it down into factor tree. There are several approaches to creating a prime factorization, but typically the 'trial method' of simply dividing small primes into the the number is often the easiest approach. Students who are trying to determine a prime factorization will be well served to have memorized the rules of divisibilty for numbers (for example, knowing that even numbers are divisible by two, or that numbers ending in zero or five are divisible by 5) as these provide a quick way to get some of the more obvious factors out and into the factorization tree.

Any number that is not prime, that is to say one that has a prime factorization with more than one prime in it, are called composite numbers. When building a factor tree in the course of creating a a prime factorization, you may reach intermediate numbers at internal branching nodes in the tree that are themselves composite numbers and whose prime factorizations are a subset of the factorization of the number you're working on.

Some of the prime factorization worksheets in this section deal with factorization of large primes. These are particularly challenging problems even with a calculator, and students may need to be prepared to research numbers to determine if they are prime or not. Of course, one way to check if a number is prime or not is to use the prime factorization calculator at the link below...

Prime Factorization CalculatorPrime factorizations are useful for determining the greatest common denominator of two numbers, or to find the least common multiple of two numbers. The prime factorization worksheets in this section are great great practice for both of these skills.