question_answer 43)

Find the HCF of the following numbers. (a) 18, 48                              (b) 30, 42                             (c) 18, 60                              (d) 27, 63 (e) 36, 84                             (i) 34, 102                             (g) 70, 105,175                   (h) 91, 112, 49 (i) 18, 54, 81                        (j) 12, 45, 75                

Answer:

                (a) Prime factorisation of \[18=\times 3\times \] Prime factorisation of      \[48=\times 2\times \times 2\times 2\] Common factors of 18 and 48 are 2 and 3. Thus, HCF of 18 and \[48=2\times 3=6\] (b) Prime factorisation of \[30=\times \times 5\] Prime factorisation of      \[42=\times \times 7\] Common factors of 30 and 42 are 2 and 3. Thus, HCF of 30 and \[42=2\times 3=6\] (c) Prime factorisation of \[18=2\times \times \] Prime factorisation of      \[60=2\times \times \times 5\] Common factors of 18 and 60 are 2 and 3. Thus, HCF of 18 and \[60=2\times 3=6\] (d) Prime factorisation of \[27=\times \times 3\] Prime factorisation of       \[63=\times \times 7\] Common factor of 27 and 63 is 3 (occurring twice) Thus, HCF of 27 and \[63=3\times 3=9\] (e) Prime factorisation of \[36=\times \times \times 3\] Prime factorisation of       \[84=\times \times \times 7\] Common factors of 36 and 84 are 2 (occurring twice) and 3. Thus, HCF of 36 and \[84=2\times 2\times 3=12\] (f) Prime factorisation of \[34=\times \] Prime factorisation of    \[102=\times \times 3\] Common factors of 34 and 102 are 2 and 17. Thus, HCF of 34 and \[102=2\times 17=34\] (g) Prime factorisation of \[70=2\times \times \] Prime factorisation of     \[105=3\times \times \] Prime factorisation of     \[175=3\times \times \] Common factors of 70, 105 and 175 are 5 and 7. Thus, HCF of 70, 105 and \[175=5\times 7=35\] (h) Prime factorisation of \[91=\times 13\] Prime factorisation of     \[112=\times 2\times 2\times 2\times 2\] Prime factorisation of      \[49=\times 7\] Common factor of 91, 112 and 49 is 7 Thus, HCF of 91, 112 and 49 = 7. (i) Prime factorisation of \[18=2\times \times \] Prime factorisation of     \[54=2\times \times \times 3\] Prime factorisation of     \[81=3\times \times \times 3\] Common factor of 18, 54 and 81 is 3 (occurring twice). Thus, HCF of 18, 54 and \[81=3\times 3=9\] (j) Prime factorisation of \[12=2\times 2\times \] Prime factorisation of      \[45=5\times 3\times \] Prime factorisation of      \[75=5\times 5\times \] Common factor of 12, 45 and 75 is 3. Thus, HCF of 12, 45 and 75 = 3