Question

Find the HCF of the following numbers.
(1) 45, 30 (2) 16, 48 (3) 39, 25 (4) 49, 56 (5) 120, 144
(6) 81, 99 (7) 24, 36 (8) 25, 75 (9) 48, 54 (10) 150, 225

Answer 1

(1)
Factors of 45: 1, 3, 5, 9, 15, 45

Factors of 30: 1, 2, 3, 5, 6, 10, 15, 30

Common factors of 45 and 30: 1, 3, 5, 15

∴ HCF of 45 and 30 = 15

(2)
Factors of 16: 1, 2, 4, 8, 16

Factors of 48: 1, 2, 3, 4, 6, 8, 12, 16, 24, 48

Common factors of 16 and 48: 1, 2, 4, 8, 16

∴ HCF of 16 and 48 = 16

(3)
Factors of 39: 1, 3, 13, 39

Factors of 25: 1, 5, 25

Common factors of 39 and 25: 1

∴ HCF of 39 and 25 = 1

(4)
Factors of 49: 1, 7, 49

Factors of 56: 1, 2, 4, 7, 8, 14, 28, 56

Common factors of 49 and 56: 1, 7

∴ HCF of 49 and 56 = 7

(5)
Factors of 120: 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120

Factors of 144: 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 48, 72, 144

Common factors of 120 and 144: 1, 2, 3, 4, 6, 8, 12, 24

∴ HCF of 120 and 144 = 24

(6)
Factors of 81: 1, 3, 9, 27, 81

Factors of 99: 1, 3, 9, 11, 33, 99

Common factors of 81 and 99: 1, 3, 9

∴ HCF of 81 and 99 = 9

(7)
Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24

Factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36

Common factors of 24 and 36: 1, 2, 3, 4, 6, 12

∴ HCF of 24 and 36 = 12

(8)
Factors of 25: 1, 5, 25

Factors of 75: 1, 3, 5, 15, 25, 75

Common factors of 25 and 75: 1, 5, 25

∴ HCF of 25 and 75 = 25

(9)
Factors of 48: 1, 2, 3, 4, 6, 8, 12, 16, 24, 48

Factors of 54: 1, 2, 3, 6, 9, 18, 27, 54

Common factors of 48 and 54: 1, 2, 3, 6

∴ HCF of 48 and 54 = 6

(10)
Factors of 150: 1, 2, 3, 5, 6, 10, 15, 25, 30, 50, 75, 150

Factors of 225: 1, 3, 5, 9, 15, 25, 45, 75, 225

Common factors of 150 and 225: 1, 3, 5, 15, 25, 75

∴ HCF of 150 and 225 = 75