Lesson 5 1 Number Theory Prime and Composite

Lesson 5. 1 Number Theory: Prime and Composite Numbers

• The set of Natural Numbers N = {1, 2, 3, 4, 5, . . . }

• Divisible – a is divisible by b if the operation of dividing a by b leaves a remainder of 0. 6|24 7|24

• Prime number – natural number greater than 1 that has only itself and 1 as factors. • Composite Numbers – natural number greater than 1 that is divisible by a number other than itself and one.

• Prime Factorization – expressing a composite as the product of prime numbers. Factor Tree Method 700 120

• What is the Greatest common Divisor of 5 & 26? • Such number pairs are said to be relatively prime.

• Greatest Common Divisor (Factor) – largest number that is a divisor (or factor) of all the numbers.

• Finding the Greatest Common Divisor of Two or More Numbers using Prime Factorizations. • 1 Write the prime factorization of each number. • 2) Select each prime factor with the smallest exponent that is common to each of the prime factorizations. • 3) Multiply the numbers from step 2.

• Find the GCD of 216 and 234

• Least common Multiple – smallest number that is divisible by all of the numbers.

• Finding LCM from prime factorization. 1) Write the prime factorization. 2) Select every prime factor that occurs, raised to the greatest power to which it occurs. 3) Multiply the numbers from step 2.

• Find the LCM of 216 and 234