Selina solutions

# Question 1

Q1) Using the common factor method, find the H.C.F. of :

(i) 16 and 35

(ii) 25 and 20

(iii) 27 and 75

(iv) 8, 12 and 18

(v) 24, 36, 45 and 60

Solution 1:

(i) F_{16}=1,\ 2,\ 4,\ 8,\ 16

F_{35}=1,\ 5,\ 7,\ 35

Common factors between 16 and 35 = 1

HCF of 16 and 35 = 1

(ii) F_{25}=1,\ 5,\ 25

F_{20}=1,\ 2,\ 4,\ 5,\ 10,\ 20

Common factors between 25 and 20 = 1, 5

HCF of 25 and 20 = 5

(iii) F_{27}=\ 1,\ 3,\ 9,\ 27

F_{75}=\ 1,\ 3,\ 5,\ 15,\ 25,\ 75

Common factors between 27 and 75 = 1, 3

HCF of 27 and 75 = 3

(iv) F_8=1,\ 2,\ 4,\ 8

F_{12}=\ 1,\ 2,\ 3,\ 4,\ 6,\ 12

F_{18}=\ 1,\ 2,\ 3,\ 6,\ 9,\ 18

Common factors between 8, 12 and 18 = 1,2

HCF of 8, 12 and 18 = 2

(v) F_{24}=1,\ 2,\ 3,\ 4,\ 6,\ 8,\ 12,\ 24

F_{36}=1,\ 2,\ 3,\ 4,\ 6,\ 9,\ 12,\ 18,\ 36

F_{45}=\ 1,\ 3,\ 5,\ 9,\ 15,\ 45

F_{60}=\ 1,\ 3,\ 4,\ 5,\ 6,\ 10,\ 12,\ 15,\ 20,\ 30,\ 60

Common factors between 24, 36, 45 and 60 = 1, 3

HCF of 24, 36, 45 and 60 = 3

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