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.
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