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GPS Standard: M6N1 Students will understand the meaning of the four arithmetic operations as related to positive rational numbers and will use these concepts to solve problems a. Apply factors and multiples EU: Factors and multiples are related in ways that are similar to the way that multiplication and division are related. EQ: How are factors and multiples related to multiplication and division? Vocabulary: Factors, Multiples, Arrays • Factors are whole numbers that are multiplied to find 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 • 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. 1 x 16 2x8 3 x ?? 4x4 3 is not a factor, so cross it out doubles = done The factors of 16 are 1,2,4,8,16 1 2 3 4 5 6 x x x x x x 18 9 6 ?? ?? 3 The factors are 1,2,3,6,9,18 Repeat! Cross it out! We’re done! 1x7 2 x ?? 3 x ?? 4 5 6 7 x x x x ?? ?? ?? 1 The only factors of 7 are 1,7 This works, but it is a repeat. We are done. • A multiple is the product of a number and any nonzero whole numbers. • Multiples are formed by multiplying a given number by the counting numbers. • The counting numbers are 1, 2, 3, 4, 5, 6, etc. • • • • • • 4x1=4 4x2=8 4 x 3 = 12 4 x 4 = 16 4 x 5 = 20 4 x 6 = 24 Counting Numbers So, the multiples of 4 are 4, 8, 12, 16, 20, 24, 28, etc. 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 • 6, 12, 18, ____, ____ • ___, 6, 9, 12, ____, ____, 21 • ___, 24, 36, 48, 60, ____ • An array is a rectangular pattern of items arranged in columns and rows.