Q. 14.7( 52 Votes )

Find the HCF of the following numbers:
(a) 18, 48 (b) 30, 42

(c) 18, 60 (d) 27, 63

(e) 36, 84 (f) 34, 102

(g) 70, 105, 175

(h) 91, 112, 49 (i) 18, 54, 81

(j) 12, 45, 75

Answer :

HCF – Highest common factor


The highest common factor of two or more numbers is the largest number that divides saparetly both the numbers.


(a) 18 and 48,




18 = 2 × 3 × 3


48 = 2 × 2 × 2 × 2 × 3


HCF = 2 × 3 = 6


(b) 30, 42




30 = 2 × 3 × 5


42 = 2 × 3 × 7


HCF = 2 × 3 = 6


(c) 18, 60




18 = 2 × 3 × 3


60 = 2 × 2 × 3 × 5


HCF = 2 × 3 =6


(d) 27, 63




27 = 3 × 3 × 3


63 = 3 × 3 × 7


HCF = 3 × 3 = 9


(e) 36, 84




36 = 2 × 2 × 3 × 3


84 = 2 × 2 × 3 × 7


HCF = 2 × 2 × 3 = 12


(f) 34, 102




34 = 2 × 17


102 = 2 × 3 × 17


HCF = 2 × 17 = 34


(g) 70, 105, 175





70 = 2 × 5 × 7


105 = 3 × 5 × 7


175 = 5 × 5 × 7


HCF = 5 × 7 = 35


(h) 91, 112, 49





91 = 7 × 13


112 = 2 × 2 × 2 × 2 × 7


49 = 7 × 7


HCF = 7


(i) 18, 54, 81





18 = 2 × 3 × 3


54 = 2 × 3 × 3 × 3


81 = 3 × 3 × 3 × 3


HCF = 3 × 3 = 9


(j) 12, 45, 75





12 = 2 × 2 × 3


45 = 3 × 3 × 5


75 = 3 × 5 × 5

HCF = 3

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