## Key Concepts

**Find the prime factorization of a composite number using the tree method.**- Find any factor pair of the given number, and use these numbers to create two branches.
- If a factor is prime, that branch is complete. Circle the prime.
- If a factor is not prime, write it as the product of a factor pair and continue the process.
- Write the composite number as the product of all the circled primes.

**Find the prime factorization of a composite number using the ladder method.**- Divide the number by the smallest prime.
- Continue dividing by that prime until it no longer divides evenly.
- Divide by the next prime until it no longer divides evenly.
- Continue until the quotient is a prime.
- Write the composite number as the product of all the primes on the sides and top of the ladder.

**Find the LCM using the prime factors method.**- Find the prime factorization of each number.
- Write each number as a product of primes, matching primes vertically when possible.
- Bring down the primes in each column.
- Multiply the factors to get the LCM.

**Find the LCM using the prime factors method.**- Find the prime factorization of each number.
- Write each number as a product of primes, matching primes vertically when possible.
- Bring down the primes in each column.
- Multiply the factors to get the LCM.

## Glossary

**multiple of a number**- A number is a multiple of [latex]n[/latex] if it is the product of a counting number and [latex]n[/latex] .

**divisibility**- If a number [latex]m[/latex] is a multiple of [latex]n[/latex] , then we say that [latex]m[/latex] is divisible by [latex]n[/latex] .

**prime number**- A prime number is a counting number greater than 1 whose only factors are 1 and itself.

**composite number**- A composite number is a counting number that is not prime.