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:
- check divisibility rules
- if not obvious yet, find the square root
- find all the prime numbers less than the square root
- 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
- first term is a perfect square
- second term is a perfect square
- they are separated by a minus sign
Factoring trinomials
- rule out any common factor
- multiply coefficient of first term by coefficient of last term
- find the factor pair of that number that adds/subtracts to equal coefficient of second term
- split the second term into 2 terms
- then factor and check
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