1. Numbers MST101

2. Number Types 1.Counting Numbers (natural numbers) 2.Whole Numbers 3.Fractions – represented by a pair of whole numbers a/b where b ≠ 0 4.Integers Positive Negative What about 0?

3. Number Types (cont.) 5.Rational numbers a/b where a and b are integers and b ≠ 0 6.Irrational numbers 7.Real numbers 8.Imaginary Numbers

4. Other ways to organize numbers Prime/Composite Odd/even Fundamental Theorem of Arithmetic Every composite number can be expressed as the product of primes in exactly one way.

5. PrimeFactorization Prime Factorization Breaking down a composite number into its primes Can use factor trees, but answers should be written as a product of primes with exponents Examples: –36 = 2 2 x 3 2 –125 = 5 3 –1176 = 2 3 x 3 1 x 7 2

6. GCD Greatest Common Divisor – given two numbers a and b, the GCD is the largest of all integers dividing both a and b Use prime factorization – GCD is the product of all primes in common with the smallest exponent used

7. TofindtheGCD To find the GCD 1.Make a factor tree 2.Select only the common factors 3.Select the smallest exponent 4.Examples: 1.gcd(75, 120) 2.gcd(42, 24)

8. LCM Least Common Multiple – the smallest of all the positive integers that are multiples of both a and b Use prime factorization the LCM will be the product of all primes, using the highest power for each prime

9. To find the LCM 1.Make a factor tree 2.Select all the factors but do not repeat the same base 3.Select the highest exponent for each base represented. 4.Examples: 1.lcm(75, 120) 2.lcm(24, 36)

10. Howdo you know you did it right? How do you know you did it right? gcd(a, b) x lcm(a, b) = a x b Check it out!!! Why?