Question
Please answer all parts of the question! Problem 1. Compute the subgroups (0), (1), (2), (3),...
Please answer all parts of the question!
Problem 1. Compute the subgroups (0), (1), (2), (3), and (4) of the additive group Zs. Find the greatest common divisor of the following pair of numbers: a) 42 and 76; b) 42 and 7: c) 42 and 21; d) 84 and 144.
Answers
2 0 Given 25 = {0,11,213,4 375 divisors of 5 are 185 co>={o} <17= {1,213,4,03 . 227 = { 214,1,3,0) <37= { 318,4,2,0) 247= {4,3,2,0,1} <07 and as are only subgroups 407@@ Ged (42,76) 76 = 4a Ci) +34 42 = 34 (1) + 8 34 = 8(4) + 2 8 = 214) +o .: Ged (42176) = 2 by Eclydion division lemna. 1 0 Ged (42,7) 7) 42 (6 sol y2 = 746) + 0 0 Ged (7,42) = 7 Ged (42,21) 42 = 21x(2) + 0 Gcd (42,21) = 21 @ God (84,144) sol 144 = 84x(4) +60 84) by (o 84 = 60 (1) + 24 60 = 2419 1+12 24) 60 (2 48 = 1244) + 0. 12) 34 (2 i Grd (B4,144) =12 760060cm 48
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