question_answer 1)

Find the common factors of (a) 4, 8 and 12                                    (b) 5, 15 and 25

Answer:

                (a) We have 4, 8 and 12 \[4=1\times 4;4=2\times 2\] \[\therefore \] Factors of 4 are 1, 2 and 4. Now, \[8=1\times 8;8=2\times 4\] \[\therefore \] Factors of 8 are 1, 2, 4 and 8. And \[~12=1\times 12;12=2\times 6;12=3\times 4\] \[\therefore \] Factors of 12 are 1, 2, 3, 4, 6 and 12. Now, all factors of \[4=,,\] all factors of \[8=,,,8\] and all factors of \[12=,,3,,6,12\] Hence, common factors of 4, 8 and 12 are 1, 2 and 4. (b) We have 5, 15 and 25 \[5=1\times 5\] \[\therefore \] Factors of 5 are 1 and 5. Now,     \[15=1\times 15;15=3\times 5\] \[\therefore \] Factors of 15 are 1, 3, 5 and 15. and        \[25=1\times 25;25=5\times 5\] \[\therefore \]  Factors of 25 are 1, 5 and 25. Now, all factors of \[5=,\] all factors of \[15=,3,,15\] and all factors of \[25=,,25\] Hence, common factors of 5, 15 and 25 are 1 and 5.