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FACTORS & MULTIPLES 1 ARRANGEMENT OF STARS Take 6 stars and arrange them in different ways 2 1 Row × 6 Stars/Row = 6 Stars 3 3 Rows × 2 Stars per row = 6 stars 4 2 Rows × 3 stars per row = 6 stars 5 6 Rows × 1 Star/Row = 6 Stars 6 As we can see, 6 can be written as product of two numbers in many ways: 6=1×6 6=2×3 6=3×2 6=6×1 1, 2, 3 and 6 are exact divisors of 6 7 ARRANGEMENT OF SOCCER BALLS Take 8 soccer balls and arrange them in different ways 8 Arrangement of 8 in different ways 1 Row × 8 Balls/Row = 8 Balls 9 2 Rows × 4 Balls / Row = 8 Balls 10 4 Rows × 2 Balls / Row = 8 Balls 11 8 Rows × 1 Ball / Row = 8 Balls 12 4 × 5 = 20 Factors Multiple 13 Factors Factors are the numbers you multiply together to get a product. For example, the product 24 has several factors. 24 = 1 x 24 24 = 2 x 12 24 = 3 x 8 24 = 4 x 6 SO, the factors are 1, 2, 3, 4, 6, 8, 12, 24 Finding Factors Start with 1 x the number. Try 2, 3, 4, etc. When you repeat your factors, cross out the repeat - you’re done at this point. If you get doubles (such as 4 x 4), then you’re done. Repeats or doubles let you know you’re done. What are the factors of 16? 1 x 16 2x8 3 x ?? 3 is not a factor, so cross it out 4x4 The factors of 16 are 1,2,4,8,16 doubles = done What are the factors of 7? 1x7 The only factors of 7 are 1,7 2 x ?? 3 x ?? 4 x ?? 5 x ?? 6 x ?? 7x1 This works, but it is a repeat. We are done. 4 × 5 = 20 Factors Multiple 18 Multiples A multiple is formed by multiplying a given number by the counting numbers. The counting numbers are 1, 2, 3, 4, 5, 6, etc. Example: List the multiples of 4: 4 4 4 4 4 4 x x x x x x 1 2 3 4 5 6 =4 =8 =12 =16 =20 =24 Counting Numbers So, the multiples of 4 are 4, 8, 12, 16, 20, 24, 28, etc. What are the first five multiples of 13? 13 x 1 =13 13 x 2 = 26 13 x 3 = 39 13 x 4 = 52 13 x 5 = 65 13, 26, 39, 52, 65 Find the Missing Multiples 24 30 6, 12, 18, ____, ____ ___, 6, 9, 12, ____, ____, 21 3 15 18 ___, 24, 36, 48, 60, ____ 12 72 Prime and Composite Numbers Prime numbers are numbers that only have two factors: one, and the number itself. EXAMPLES: 3, 5, 7, 11, 31 Composite numbers have more than two factors. EXAMPLES: 6, 18, 30, 100 POINTS TO REMEMBER • 1 is a factor of every number. • Every factor of a number is an exact divisor of that number. • Every factor is less than or equal to the given number. • Number of factors of a given number are finite. 24 POINTS TO REMEMBER contd • Every multiple of a number is greater than or equal to that number. • The number of multiples of a given number is infinite. • Every number is a multiple of itself. 25 FACTOR OR MULTIPLE? For each of numbers in the statements, select either multiple [M] or factor [F] 34 × 5 = 170 [F] [M] 25 [F] [M] × [F] [M] 90 [F] [M] × [F] [M] 45 × 7 [F] [M] 6 [F] [M] × = 100 [F] [M] 10 = 900 [F] [M] [F] [M] 4 [F] [M] [F] [M] = 270 [F] [M] 30 = 210 [F] [M] [F] [M] 26 State whether the following statements are TRUE or FALSE 1. 1 is a factor of every number. F T 2. The largest factor of any number is the number itself. F T 3. Number of factors of a given number is infinite. F T 4.The number of multiples of 5 is 10. F T 5.The factors of 65 are 1, 5 and 13 only. F T ( Click ‘F’ for false and ‘T’ for true ) 27 THANK YOU 28 CORRECT 29 WRONG 30