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Notes 1.5 – Factors and Divisibility Patterns I. Review Natural Numbers: 1, 2,3, 4,... Whole Numbers: 0,1, 2,3, 4,... Integers: ..., 2, 1, 0,1, 2,... 1 Divisible What does it mean for one number to divide evenly into another? What is the remainder when 8 is divided by 3? When you divide the numbers the remainder is 0. 2 What does the remainder have to do with divisibility? If the remainder is zero then the number is divisible by the divisor. Modeling Divisibility: Arrange 6 tokens in a rectangle with 2 rows to show that 6 is divisible by two. 2 More Modeling Use tokens to show 7 divided by 2. Factors A number is a _______ factor of a given number if it ________ divides into the second number ________. evenly Example: 1) Which of the following numbers are factors of 12? a) 24 b) 3 c) 12 d) 4 e) 5 3 2) Name the other factors of 12: 1,2, and 6 3) What are the factors of 48? 1,2,3,4,6,8,12,16,24,48 ______ and the ___________ NUMBER itself are factors of 1 any given number. Eric rents a booth at a crafts fair. He is allowed to set up 36 square feet in any way that he wants. Eric decides to make his booth 9 feet long and 4 feet wide. 1) What is the total area of Eric’s booth? A 4 9 36 a) A = lw b) Using only natural numbers what are all the possible side that Eric’s booth could have? w l A 1 36 36 2 3 18 36 12 36 4 6 9 6 36 36 4 Primes, Composites, and Squares A _________ PRIME number is a natural number with exactly two factors, itself and one. A ____________number is a natural number that is COMPOSITE greater than 2 and is not prime. A composite number has more than ____ 2 factors. Examples 1) Circle the following numbers that are prime: a) 51 b) 37 c) 2 d) 1 e) 17 2) Circle the composite numbers: a.) 21 b) 17 c) 50 d) 39 e) 1 (_____ is the only number that is neither prime nor 1 composite.) 5 3) What are the factors of 19? Is it prime or composite? 1,19 PRIME 4) What are the first ten prime numbers? 2 , 3 , 5 , 7 , 11 , 13 , 17 , 19 , 23 , 29 What are the factors of 4? How many factors does it have? 1,2,4 3 1,5,25 What are the factors of 25? How many factors does it have? 3 What are the factors of 36? 1,2,3,4,6,9,12,18,36 9 How many factors does it have? A _________ SQUARE number has an odd number of factors and can be represented as a square with an area equal to the square number. 6 Divisibility Patterns Pattern Examples Div. by 2 Last digit is even Div. by 10 Last digit is 0 10, 140, 900 Div. by 5 Last digit is 0 or 5 10, 145, 980 Div. by 3 Sum of digits is by 3 27, 96, 144 Div. by 6 by 2 and 3 42, 132, 960 Div. by 9 Sum of digits is by 9 4, 38, 490 72, 144, 945 Homework: pages 41-42#’s 1, 2, 4, 6-8, 10-42 even. 7