Question

d. 18, 26 1. Find the HCF of the following numbers by listing factors method. a. 12,46 b. 25, 40, 45 C. 14, 30,28 e. 10, 15, 35 f. 32, 39, 44 2. Find the HCF of the following numbers by the prime factorisation method. a. 28, 42, and 49 b. 40, 56, and 64 c. 32, 48, and 80 d. 44, 55, and 99 e. 36, 54, and 90 f. 42, 70, and 98 66​

Answer 1

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Answer 2

Answer:

Ncert solutions

Mathematics

Chapters in NCERT Solutions - Mathematics, Class 6

Exercises in Playing With Numbers

Question 2

Q1) Find the HCF of the following numbers :

(i) 18, 48 (ii) 30, 42 (iii) 18, 60 (iv) 27, 63

(v) 36, 84 (vi) 34, 102 (vii) 70, 105, 175

(viii) 91, 112, 49 (ix) 18, 54, 81 (x) 12, 45, 75

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SOLUTION:

i) 18,48

18=2\times3\times318=2×3×3

48=2\times2\times2\times2\times348=2×2×2×2×3

The common factor of 18 and 48 are 2,3. thus, HCF of 18 and 48 is2\times3=62×3=6

ii) 30,42

30=2\times3\times530=2×3×5

42=2\times3\times742=2×3×7

The common factor of 30 and 42 are 2 and 3

thus, HCF of 30,42 are 2\times3=62×3=6

iii) 18,60

18=2\times3\times318=2×3×3

60=2\times2\times3\times560=2×2×3×5

The common factor of 18 and 60 are 2,3. thus, HCF of 18 and 60 are 2\times3=62×3=6

iv) 27, 63

27=3\times3\times327=3×3×363=3\times3\times763=3×3×7

The common factor for 27 and 63 is 3

thus, HCF of 27 and 63 is 3\times3=93×3=9

v) 36,84

36=2\times2\times3\times336=2×2×3×384=2\times2\times3\times784=2×2×3×7

The common factor of 36 and 84 is 2\times32×3

thus, HCF of 36 and 84 is 2\times2\times3=122×2×3=12

vi) 34, 102

34=2\times1734=2×17102=2\times3\times17102=2×3×17

The common factor in 34 and 102 is 2, 17.

thus, HCF for 34 and 102 is 2\times17=342×17=34

vi) 70, 105, 175

70=2\times5\times770=2×5×7

105=3\times5\times7105=3×5×7

175=5\times5\times7175=5×5×7

The common factor in 70, 105 and 175 are 5, 7.

thus, HCF for 70,105 and 175 is 5\times7=355×7=35

vii) 91,112,49



91=7\times1391=7×13112=2\times2\times2\times2\times7112=2×2×2×2×749=7\times749=7×7

The common factors of 91, 112, and 49 are 7.

therefore, HCF of 91, 112 and 49 are 7.

viii) 18, 54,81



18=2\times3\times318=2×3×354=2\times3\times3\times354=2×3×3×381=3\times3\times3\times381=3×3×3×3

therefore common factors between 18, 54, 81 is 3X3=9

xi) 12,45,75

therefore, the coomon factor is 3.

HCF of 12,45,75 is