Find the GCF of each list of numbers:(a) 21 and 140, (b) 24, 60, and 96, and(с) 9, 10, and 30We will prime factor each number in the list. Then we will identify the commonprime 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 =• 7140= 2 •5 : 7This 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 •• 3This can be written as 23 · 3.60 = 2 • 2•3•This can be written as 22 · 3•5.96 = 2 • 2•2•2•• 3This 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 commonprime 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 =310 = 2 •30 =• 3• 5Find 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)

The largest number, which is the factor of two or more number is called the Greatest Common Factor…

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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

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018

18th Edition

ISBN:9780079039897

Author:Carter

Publisher:Carter

Chapter8: Polynomials

Section8.7: Factoring Special Products

Problem 34PPS

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Question

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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