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Find the GCF of each list of numbers: (a) 26 and 77, (b) 25, 27, and 90, and (c) 40, 60, and 80

Find the GCF of each list of numbers: (a) 26 and 77, (b) 25, 27, and 90, and (c) 40, 60, and 80

Algebra and Trigonometry (6th Edition)
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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Find the GCF of each list of numbers: (a) 21 and 140, (b) 24, 60, and 96, and (с) 9, 10, and 30 We will prime factor each number in the list. Then we will identify the common prime factors and find their product. The product of the common prime factors is the GCF of the numbers in the list. (a) The prime factorization of each number is shown: 21 = • 7 140 = 2 • 5 : 7 This can be written as 22.5•7. Since the only prime factor common to 21 and 140 is 7, the GCF of 21 and 140 is 7. (b) To find the GCF of three numbers, we proceed in a similar way by first finding the prime factorization of each number in the list. 24 = 2 • 2 • • 3 This can be written as 23 · 3. 60 = 2 • 2•3• This can be written as 22 · 3•5. 96 = 2 • 2•2•2• • 3 This can be written as 25• 3. The highlighting shows that 24, 60, and 96 have two factors of 2 and one factor of 3 in common. The GCF of 24, 60, and 96 is the product of their common prime factors. GCF = 2· 2• 3 = 22 · 3 = (c) Since there are no prime factors common to 9, 10, and 30, their GCF is 1. 9 = 3 10 = 2 • 30 = • 3• 5 Find the GCF of each list of numbers: (a) 26 and 77, (b) 25, 27, and 90, and (c) 40, 60, and 80 (a) (b) (c)
Transcribed Image Text:Find the GCF of each list of numbers: (a) 21 and 140, (b) 24, 60, and 96, and (с) 9, 10, and 30 We will prime factor each number in the list. Then we will identify the common prime factors and find their product. The product of the common prime factors is the GCF of the numbers in the list. (a) The prime factorization of each number is shown: 21 = • 7 140 = 2 • 5 : 7 This can be written as 22.5•7. Since the only prime factor common to 21 and 140 is 7, the GCF of 21 and 140 is 7. (b) To find the GCF of three numbers, we proceed in a similar way by first finding the prime factorization of each number in the list. 24 = 2 • 2 • • 3 This can be written as 23 · 3. 60 = 2 • 2•3• This can be written as 22 · 3•5. 96 = 2 • 2•2•2• • 3 This can be written as 25• 3. The highlighting shows that 24, 60, and 96 have two factors of 2 and one factor of 3 in common. The GCF of 24, 60, and 96 is the product of their common prime factors. GCF = 2· 2• 3 = 22 · 3 = (c) Since there are no prime factors common to 9, 10, and 30, their GCF is 1. 9 = 3 10 = 2 • 30 = • 3• 5 Find the GCF of each list of numbers: (a) 26 and 77, (b) 25, 27, and 90, and (c) 40, 60, and 80 (a) (b) (c)
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