FPC10 3.1 - Scan.pdf
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# Foundations and Pre-Calculus 10 - Section 3.1 Factors and Multiples of Whole Numbers ## Warmup Part 1 1. List all the factors of 24 and 40: * **24:** 1, 2, 3, 4, 6, 8, 12, 24 * **40:** 1, 2, 4, 5, 8, 10, 20, 40 2. Write as a product of primes: a. 24: 2 x 2 x 2 x 3 = $2^3$ x 3 b. 40...
# Foundations and Pre-Calculus 10 - Section 3.1 Factors and Multiples of Whole Numbers ## Warmup Part 1 1. List all the factors of 24 and 40: * **24:** 1, 2, 3, 4, 6, 8, 12, 24 * **40:** 1, 2, 4, 5, 8, 10, 20, 40 2. Write as a product of primes: a. 24: 2 x 2 x 2 x 3 = $2^3$ x 3 b. 40: 2 x 2 x 2 x 5 = $2^3$ x 5 3. Simplify: $\frac{24}{40} = \frac{3}{5}$ * What did you do when you reduced/simplified the fraction? Divided numerator and denominator by the common factor. * Rewrite the numerator and denominator in their prime factored form then simplify: $\frac{2^3 \times 3}{2^3\times 5} = \frac{3}{5}$ ## Definitions - **Prime number:** A whole number that can only be divided by one and itself. - **Prime factorization:** Breaking up a number into its prime factors. - **Greatest Common Factor (GCF):** The greatest whole number that each number from a series of numbers can be divided by to give whole numbers. ## Example 1: Find the greatest common factor (GCF) of each of the following: a. 126 and 144 * 2 | 126, 144 * 3 | 63, 72 * 3 | 21, 24 * 7, 8 * GCF: 2 x 3 x 3 = 18 b. 56, 112, 168 * 2 | 56, 112, 168 * 2 | 28, 56, 84 * 2 | 14, 28, 42 * 7 | 7, 14, 21 * 1, 2, 3 * GCF: 2 x 2 x 2 x 7 = 56 ## Warmup Part 2 1. Write as a product of primes: a. 150: 2 x 5 x 5 x 3 = 2 x $5^2$ x 3 b. 60: 2 x 2 x 5 x 3 = $2^2$ x 5 x 3 2. Draw a Venn Diagram with the prime factors of 150 and 60. Calculate the product of all the numbers in the Venn Diagram - factors that both have in common should be in the middle area only once. * The Venn Diagram would show the common factors 2, 3, and 5 in the overlapping section, with 2 and 5 in the 60 section only and 5 in the 150 section only. * The calculation is: 2 x 5 x 5 x 3 x 2 = 300 ## Example 2: Find the least common multiple (LCM) of each of the following: - **Least Common Multiple (LCM):** The lowest multiple that a set of numbers have in common. a. 24, 60: * 2 | 24, 60 * 2 | 12, 30 * 3 | 6, 15 * 2, 5 * LCM: 2 x 2 x 3 x 2 x 5 = 120 b. 28, 42, 63: * 2 | 28, 42, 63 * 3 | 14, 21, 63 * 7 | 14, 7, 21 * 2, 1, 3 * LCM: 2 x 3 x 7 x 2 x 1 x 3 = 252 ## Assignment: page 140 # 6ace, 7, 8 – 11 ace, 14, 15-16 ce, 17
