question_answer 28)

Which of the following numbers are co-prime? (a) 18 and 35                      (b) 15 and 37                      (c) 30 and 415                    (d) 17 and 68   (e) 216 and 215                 (f) 81 and 16 TIPS Firstly, write the factors of given numbers. If two numbers have only 1 as common factor, then they are called co-prime numbers otherwise not.

Answer:

                (a) We have, 18 and 35 \[18=1\times 18;18=2\times 9;18=3\times 6\] Factors of 18 are 1, 2, 3, 6, 9 and 18. and        \[35=1\times 35;35=5\times 7\] Factors of 35 are 1, 5, 7 and 35. \[\because \] Common factor of 18 and 35 is only 1. So, 18 and 35 are co-prime numbers. (b) We have, 15 and 37 \[15=1\times 15;15=3\times 5\] Factors of 15 are 1, 3, 5 and 15. and        \[37=1\times 37\] Factors of 37 are I and 37. \[\because \] Common factor of 15 and 37 is only 1. So, 15 and 37 are co-prime numbers. (c) We have, 30 and 415 \[30=1\times 30;30=2\times 15;30=3\times 10;30=5\times 6\] Factors of 30 are I, 2, 3, 5, 6, 10, 15 and 30. and        \[415=1\times 415;415=5\times 83\] Factors of 415 are 1, 5, 83 and 415. \[\because \] Common factors of 30 and 415 are 1 and 5. So, 30 and 415 are not co-prime numbers. (d) We have, 17 and 68 \[17=1\times 17\] Factors of 17 are 1 and 17.                         and        \[68=1\times 68;68=2\times 34;68=4\times 17\]   \[\therefore \] Factors of 68 are 1, 2, 4, 17, 34 and 68. \[\because \] Common factors of 17 and 68 are 1 and 17. So, 17 and 68 are not co-prime numbers. (e) We have, 216 and 215                                             \[216=6\times 36;216=8\times 27;216=9\times 24;216=12\times 18~~~~~~~~~~~~~~~\] Factors of 216 are 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 27, 36, 54, 72, 108 and 216. and        \[215=1\times 215;\text{ }215=5\times 43\] Factors of 215 are 1, 5, 43 and 215 \[\because \] Common factor of 216 and 215 is only 1. So, 216 and 215 are co-prime numbers. (f) We have, 81 and 16 \[81=1\times 81;81=3\times 27;81=9\times 9~\] Factors of 81 are 1, 3, 9, 27 and 81.                                   and        \[16=1\times 16;16=2\times 8;16=4\times 4\] Factors of 16 are 1, 2, 4, 8 and 16. \[\because \] Common factor of 81 and 16 is only 1. So, 81 and 16 are co-prime numbers.