1. 1.2 Factors and Multiples Mme DiMarco

2.  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

3.  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! 7 6 18 12 20 15 8 Abundant Deficient Perfect NumberFactorsSum of Factors

4.  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, 1821 121, 2, 3, 4, 6, 1216 201, 2, 4, 5, 10, 2022 151, 3, 5, 159 71,71 81,2,4,87 61,2,3,66

5.  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) 1 + 2+ 4 + 5 + 10 = 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) 1 + 3 + 5 = 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) 1 + 2 + 3 = 6  6 = 6, therefore 6 is a perfect number Abundant, Deficient and Perfect Numbers

6. 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

7.  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

8.  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

9.  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

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