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4. (a) Find the greatest common divisor of a = 12345 and b = 54321 and express it as a linear combination of a and b. (b) Find integers x, y such that 12345x + 54321y = 9. (c) Find the least common multiple of a = 12345 and b = 54321. 1. (a) Find and express the greatest common divisor of 48 and 126 as a linear combination of these numbers. let α = 126 and b=48 2 48√126 96 30 30√48 30 12/27/28/0-180/2 -12dro 1₁ = 30 = a- =a-2b √2=18= 48-1.30 18 √30 13=12= 12V 18 ① = b - (a-2b) = -a+3b ① 30-1.18 Д = a-2b- (-a+3b) = 29-56 ① 14= 6 = 18 1.12 - =-a+3b-(2a-5b) = -39+86 =6 √5=0 12 and 126.48)= 6=-3(126) +8 (48) ①

4. (a) Find the greatest common divisor of a = 12345 and b = 54321 and express it as a linear combination of a and b. (b) Find integers x, y such that 12345x + 54321y = 9. (c) Find the least common multiple of a = 12345 and b = 54321. 1. (a) Find and express the greatest common divisor of 48 and 126 as a linear combination of these numbers. let α = 126 and b=48 2 48√126 96 30 30√48 30 12/27/28/0-180/2 -12dro 1₁ = 30 = a- =a-2b √2=18= 48-1.30 18 √30 13=12= 12V 18 ① = b - (a-2b) = -a+3b ① 30-1.18 Д = a-2b- (-a+3b) = 29-56 ① 14= 6 = 18 1.12 - =-a+3b-(2a-5b) = -39+86 =6 √5=0 12 and 126.48)= 6=-3(126) +8 (48) ①

Algebra: Structure And Method, Book 1
Algebra: Structure And Method, Book 1
(REV)00th Edition
ISBN:9780395977224
Author:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole
Publisher:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole
Chapter5: Factoring Polynomials
Section5.7: Factoring Pattern For X2+bx+c, C Positive
Problem 5OE
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4. (a) Find the greatest common divisor of a = 12345 and b = 54321 and express it as a linear combination of a and b. (b) Find integers x, y such that 12345x + 54321y = 9. (c) Find the least common multiple of a = 12345 and b = 54321.
Transcribed Image Text:4. (a) Find the greatest common divisor of a = 12345 and b = 54321 and express it as a linear combination of a and b. (b) Find integers x, y such that 12345x + 54321y = 9. (c) Find the least common multiple of a = 12345 and b = 54321.
1. (a) Find and express the greatest common divisor of 48 and 126 as a linear combination of these numbers. let α = 126 and b=48 2 48√126 96 30 30√48 30 12/27/28/0-180/2 -12dro 1₁ = 30 = a- =a-2b √2=18= 48-1.30 18 √30 13=12= 12V 18 ① = b - (a-2b) = -a+3b ① 30-1.18 Д = a-2b- (-a+3b) = 29-56 ① 14= 6 = 18 1.12 - =-a+3b-(2a-5b) = -39+86 =6 √5=0 12 and 126.48)= 6=-3(126) +8 (48) ①
Transcribed Image Text:1. (a) Find and express the greatest common divisor of 48 and 126 as a linear combination of these numbers. let α = 126 and b=48 2 48√126 96 30 30√48 30 12/27/28/0-180/2 -12dro 1₁ = 30 = a- =a-2b √2=18= 48-1.30 18 √30 13=12= 12V 18 ① = b - (a-2b) = -a+3b ① 30-1.18 Д = a-2b- (-a+3b) = 29-56 ① 14= 6 = 18 1.12 - =-a+3b-(2a-5b) = -39+86 =6 √5=0 12 and 126.48)= 6=-3(126) +8 (48) ①
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