question_answer 1)

Find the common factors of (a) 20 and 28                      (b) 15 and 25                      (c) 35 and 50                       (d) 56 and 120

Answer:

                (a) Factors of 20 and 28 are as follows: \[20=1\,\,\times \,\,20;\text{ }20=2\times 10;\text{ }20\text{ = }4\times 5\] and        \[28=1\,\,\times \,\,28;\text{ }28=2\times 14;\text{ }28=4\times 7\] Now, all factors of \[20=,2,,5,10,20\] and all factors of \[28=,2,,7,14,28\] \[\therefore \] Common factors = 1, 2, 4 Hence, common factors of 20 and 28 are 1, 2 and 4. (b) Factors of 15 and 25 are as follows: \[15=1\,\,\times \,\,15;\,\,15=3\times 5\] and        \[25=1\times 25;\text{ }25\text{ = }5\times 5\] Now, all factors of \[15=,3,,15\] and all factors of \[25=,,25\] \[\therefore \] Common factors = 1, 5 Hence, common factors of 15 and 25 are 1 and 5. (c) Factors of 35 and 50 are as follows: \[35=1\text{ }\times 35;\text{ }35=5\times 7\] and        \[50=1\times 50;\,\,50=2\times 25;\,\,50=5\times 10\] Now, all factors of \[35=,,7\] and all factors of \[50=,2,,10,25,50\] \[\therefore \] Common factors = 1, 5 Hence, common factors of 35 and 50 are 1 and 5. (d) Factors of 56 and 120 are as follows: \[56=1\times 56;\text{ }56=2\times 28;\text{ }56=4\times 14;\text{ }56=7\times 8\] and        \[20=1\times 1\text{ }20;\,\,120=2\times 60;\,\,120=3\,\times 40;\,\,120=4\times 30\] \[120=5\text{ }\times 24;\text{ }120=6\times 20;\text{ }120=8\times 15;\text{ }120=10\times 12\] Now, all factors of  \[56=,,,7,,14,28,56\] and all factors of  \[120=,,3,,5,6,10,12,15,20\] 24, 30, 40, 60, 120 \[\therefore \] Common factors = 1, 2, 4, 8 Hence, common factors of 56 and 120 are 1, 2, 4 and 8.