Pre-Algebra
1st Edition
ISBN: 9780618800766
Author: Ron Larson, Lee Stiff, Laurie Boswell, Timothy Kanold
Publisher: Houghton Mifflin-High School
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Question
Chapter 4.2, Problem 50E
To determine
To find the GCF of a and b and explain it.
Expert Solution & Answer
Answer to Problem 50E
‘a’ is the GCF of ‘a’ and ‘b’.
Explanation of Solution
Given Information:a and b are non zero whole numbers and a is a factor of b .
Formula Used:if a is a factor of b, then the GCF between the two numbers will be a. This is because, as ‘a’ is a factor of ‘b’, then ‘a’ cannot have a factor which is greater than itself.
Calculation:
To prove this, lets take 3 examples.
ExampleI Lets assume a=6 & b=42. Now
The factors of 6 are: 1, 2, 3, 6
The factors of 42 are: 1, 2, 3, 6, 7, 14, 21, 42
Then the greatest common factor is 6, i.e. ‘a’.
ExampleII Lets assume a=7 & b=42 Now
The factors of 7 are: 1, 7
The factors of 42 are: 1, 2, 3, 6, 7, 14, 21, 42
Then the greatest common factor is 7, i.e. ‘a’.
ExampleIII Lets assume a=8 & b=48 . Now
The factors of 8 are: 1, 2, 4, 8
The factors of 48 are: 1, 2, 3, 4, 6, 8, 12, 16, 24, 48
Then the greatest common factor is 8, i.e. ‘a’.
Therefore, for all 3 values of ‘a’ i.e. 6, 7, and 8, the GCF for all three numbers were 6, 7 and 8 respectively. By this can conclude that a number which is a factor of another number, is the GCF between the two of them.
Hence proved.
Chapter 4 Solutions
Pre-Algebra
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- Use the graph of y = f(x) to answer the following. 3- 2 -4 -2 -1 1 2 3 4 -1 2 m -3- + (d) Find all x for which f(x) = -2. If there is more than one value, separate them with commas or write your answer in interval notation, if necessary. Select "None", if applicable. Value(s) of x for which f(x)=-2: | (0,0) (0,0) (0,0) (0,0) 0,0... -00 None (h) Determine the range of f. The range is (0,0) Garrow_forwardWhat is g(f(4))arrow_forward10) Multiply (8m + 3)² A) 8m²+11m+6 B) m² + 48m+9 C) 64m²+48m+9 D) 16m²+11m+6arrow_forward
- Let R be field and X= R³/s Vector space over R M=(a,b,c)labic, e Rra+b= 3- <3 Show that Ms and why with proof. 1) is convexset and affine set of botost ii) is blanced set and symmetirs set of x iii) is hy per space and hyper plane ofx or hot iii) find f:MR st kerf = M 18/103 and finnd fiM→R/{0} st M= {xEX, f(t) = x, texiαER? jiii) show that Mis Maxsubspace or not and Mis a max. affine set or not.arrow_forwardFind The partial fraction decomposition for each The following 2× B) (x+3) a 3 6 X-3x+2x-6arrow_forward1) Find the partial feraction decomposition for each of 5- X 2 2x+x-1 The following: 3 B) 3 X + 3xarrow_forward
- Kate, Luke, Mary and Nancy are sharing a cake. The cake had previously been divided into four slices (s1, s2, s3 and s4). The following table shows the values of the slices in the eyes of each player. What is fair share to nancy? S1 S2 S3 S4 Kate $4.00 $6.00 $6.00 $4.00 Luke $5.30 $5.00 $5.25 $5.45 Mary $4.25 $4.50 $3.50 $3.75 Nancy $6.00 $4.00 $4.00 $6.00arrow_forwardKate, Luke, Mary and Nancy are sharing a cake. The cake had previously been divided into four slices (s1, s2, s3 and s4). The following table shows the values of the slices in the eyes of each player. S1 S2 S3 S4 Kate $4.00 $6.00 $6.00 $4.00 Luke $5.30 $5.00 $5.25 $5.45 Mary $4.25 $4.50 $3.50 $3.75 Nancy $6.00 $4.00 $4.00 $6.00 how much is the cak worth to maryarrow_forwardKate, Luke, Mary and Nancy are sharing a cake. The cake had previously been divided into four slices (s1, s2, s3 and s4). The following table shows the values of the slices in the eyes of each player. What is the threshold of fair share for Luke? S1 S2 S3 S4 Kate $4.00 $6.00 $6.00 $4.00 Luke $5.30 $5.00 $5.25 $5.45 Mary $4.25 $4.50 $3.50 $3.75 Nancy $6.00 $4.00 $4.00 $6.00arrow_forward
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