Question

. Use prime factorisation method to determine
the HCF of each of the following:
(i) 12, 18 (ii) 22, 34 (iii) 144, 100​

Answer 1

Answer:

A) 12

12 divides by 2    12 = 6 x 2

12 = 2 x 6

6 divides by 2    6 = 3 x 2

6 = 2 x 2 x 3

2, 3 is a prime number, therefore no further factorization is possible, So prime factorization of 12 are: 2 x 2 x 3

B) 18

18 divides by 2    18 = 9 x 2

18 = 2 x 9

9 divides by 3    9 = 3 x 3

9 = 2 x 3 x 3

2, 3 is a prime number, therefore no further factorization is possible, So prime factorization of 18 are: 2 x 3 x 3

C)   22

22

22 divides by 2    22 = 11 x 2

22 = 2 x 11

2, 11 is a prime number, therefore no further factorization is possible, So prime factorization of 22 are: 2 x 11

D)  34

34

34 divides by 2    34 = 17 x 2

34 = 2 x 17

2, 17 is a prime number, therefore no further factorization is possible, So prime factorization of 34 are: 2 x 17

E) 144

144

144 divides by 2    144 = 72 x 2

144 = 2 x 72

72 divides by 2    72 = 36 x 2

72 = 2 x 2 x 36

36 divides by 2    36 = 18 x 2

36 = 2 x 2 x 2 x 18

18 divides by 2    18 = 9 x 2

18 = 2 x 2 x 2 x 2 x 9

9 divides by 3    9 = 3 x 3

9 = 2 x 2 x 2 x 2 x 3 x 3

2, 3 is a prime number, therefore no further factorization is possible, So prime factorization of 144 are: 2 x 2 x 2 x 2 x 3 x 3

F) 100

100

100 divides by 2    100 = 50 x 2

100 = 2 x 50

50 divides by 2    50 = 25 x 2

50 = 2 x 2 x 25

25 divides by 5    25 = 5 x 5

25 = 2 x 2 x 5 x 5

2, 5 is a prime number, therefore no further factorization is possible, So prime factorization of 100 are: 2 x 2 x 5 x 5

Hope it helps you

Step-by-step explanation: