Prime number: a number that is divisible by only 1 and itself.

Composite number: a number that has a factor other than 1 or itself.

1 is neither prime nor composite.

How to tell if a number is prime:

1. check divisibility rules

2. if not obvious yet, find the square root

3. find all the prime numbers less than the square root

4. if none of the primes are a factor, then the original number is prime

Calculating the Least Common Multiple

• includes each factor the greatest number of times it occurs

ex. prime factorization of 20 = 2x2x5 and 30 = 2x3x5

LCM of 20 and 30 = 2x2x3x5

LCM = 60

Calculating the Greatest Common Factor

• find all similar factors and put them together

ex. prime factorization of 2940 = 2x2x3x5x7x7 and 3150 = 2x3x3x5x5x7

GCF of 2940 and 3150 = 2x3x5x7

GCF = 210

Perfect square binomials

1. first term is a perfect square

2. second term is a perfect square

3. they are separated by a minus sign

Factoring trinomials

1. rule out any common factor

2. multiply coefficient of first term by coefficient of last term

3. find the factor pair of that number that adds/subtracts to equal coefficient of second term

4. split the second term into 2 terms

5. then factor and check