1.2 Factors and Multiples Mme DiMarco

 Learning Goal: the focus of today’s lesson is to become familiarized with generating factors and multiples of given numbers.  We will be exploring ways in which numbers can describe other numbers Learning Goal

 Analyse the numbers in the circles below.  Use a table to record the factors of each number.  Find the sum of the remaining factors (not including the number itself as a factor) Explore! Abundant Deficient Perfect NumberFactorsSum of Factors

 Why do you think a number is called “ abundant ”, “deficient” or “perfect”? Results? NumberFactorsSum of Factors (not including number itself) 181,2, 3, 6, 9, , 2, 3, 4, 6, , 2, 4, 5, 10, , 3, 5, ,71 81,2,4,87 61,2,3,66

 Abundant Number: the sum of all factors (not including the number itself) is GREATER than the number itself  Example: 20  Factors (1, 2, 4, 5, 10, 20)  Sum of factors (excluding 20) = 22  22 > 20, therefore 20 is abundant  Deficient Number: the sum of all factors (not including the number itself) is LESS than the number itself  Example: 15  Factors (1, 3, 5, 15)  Sum of factors (excluding 15) = 9  9 < 15, therefore15 is deficient  Perfect Number: the sum of all factors (not including the number itself) is EQUAL to the number itself  Example: 6  Factors: 1, 2, 3, 6  Sum of factors (excluding 6) = 6  6 = 6, therefore 6 is a perfect number Abundant, Deficient and Perfect Numbers

Recall…  Factor: a number that divides exactly into another number  Example: the factors of 6 are 1, 2, 3 and 6  Prime Number: a number with only 2 factors, itself and 1.  Examples: 2, 3 and 5  Composite Number: a number with more than 2 factors.  Examples: 8, 16 and 20  Common Factors: factors that are the same for 2 numbers Factors

 Greatest common factor: the greatest number that divides into each number in a set.  What is the greatest common factor of 12 and 30?  Step 1: find all of the factors of 12 and 30  12: 1, 2, 3, 4, 6, 12  30: 1, 2, 3, 5, 6, 10, 15, 30  Step 2: highlight/circle all factors in common  Factors in common: 1, 2, 3, 6  Step 3: find the highest common factor  GCF: 6 Greatest Common Factor

 Multiples: found by multiplying the number by 1, 2, 3 and so on or by skip counting  Multiples of 10: 10, 20, 30 40, 50 …  Common Multiples: multiples that are the same for two numbers  Lowest Common Multiple (LCM): the lowest multiple that is that same for two numbers Multiples

 Step 1: list the multiples of each number  Multiples of 10: 10, 20, 30, 40, 50..  Multiples of 5: 5, 10, 15, 20..  Step 2: find the lowest common multiple among those that are in common  Multiples of 10: 10, 20, 30, 40, 50..  Multiples of 5: 5, 10, 15, 20.. Finding the Lowest Common Multiple

 Pages 16 – 17  Questions 1 – 6, 8, 9 Homework