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Prime Time Notes Factors Factors: a number that can be multiplied to get another number Example: 5 is a factor of 30 Factor pairs: two numbers that can be multiplied together to get another number Example: 5 and 6 is a factor pair of 30 Finding Factors: use the division test and test every number to write down factor pairs until you reach a number that is already written as a factor. Example: Find the factors of 30 Always start with 1 and the number itself 1, ,30 Then try other numbers using divisibility rules to help 1, 2, 3, 5, 6, 10, 15, 30 Prime number: a number with exactly 2 factors, one and the number itself Composite number: a number with more than 2 factors Multiples Multiples: a number that can be gotten by multiplying the original number Example: 30 is a multiple of 5 Finding multiples: multiply the number by 1, 2, 3, etc. continuing until you have the desired number of multiples. Greatest Common Factor: the biggest factor shared by two numbers Example: Find the GCF of 12 and 30 12: 1, 2, 3, 4, 6, 12 30: 1, 2, 3, 5, 6, 10, 15, 30 Since 6 is the largest number on both lists, 6 is the GCF. Least Common Multiple: the smallest multiple shared by two numbers [note: If the numbers are relatively prime (do not share any factors but 1) their LCM will be the product of the number. Ie. The LCM of 5 and 11 is 5x11=55.) Example: Find the LCM of 4 and 6 4: 4, 8, 12, 16, 20,… 6: 6, 12, 18, 24, … Since 12 is the smallest number on both lists, 12 is the LCM. Square numbers: any number multiplied by itself makes a square number Example: 16 is a square number because 4 x 4 = 16 List of square numbers from 1 to 100: 1, 4, 9, 14, 25, 36, 47, 64, 81, 100 Order of Operations 1. Parentheses 2. Exponents 3. Multiplication and Division from left to right 4. Addition and Subtraction from left to right Example: 12 ÷ 2 x 3 – 4 + 23 + (2+3x1) 12÷ 2 x 3 – 4 + 23 + (2 +3) 12 ÷ 2 x 3 – 4 + 23 + 5 12 ÷ 2 x 3 – 4 + 8 + 5 6x3–4+8+5 18 – 4 +8 + 5 14 + 8 + 5 22 + 5 27 Prime Factorization: A number written as a product of prime numbers. A factor tree is a good way to find prime factorization. The prime factorization of 100 =2 x 2 x 5 x 5 (expanded form) And 100 = 22 x 52 (exponential form)