Class 6 Mathematics Sindh Textbook Exercise 3.4 Solved Notes

Exercise 3.4 Solved

Question 1

Find the HCF by Prime Factorization Method.

(i) 50, 75

50 = 2 × 5²

75 = 3 × 5²

HCF = 5² = 25

(ii) 98, 196

98 = 2 × 7²

196 = 2² × 7²

HCF = 2 × 7² = 98

(iii) 144, 198

144 = 2⁴ × 3²

198 = 2 × 3² × 11

HCF = 2 × 3² = 18

(iv) 120, 144, 204

120 = 2³ × 3 × 5

144 = 2⁴ × 3²

204 = 2² × 3 × 17

HCF = 2² × 3 = 12

(v) 106, 159, 265

106 = 2 × 53

159 = 3 × 53

265 = 5 × 53

HCF = 53

(vi) 12, 48, 36, 24

12 = 2² × 3

48 = 2⁴ × 3

36 = 2² × 3²

24 = 2³ × 3

HCF = 2² × 3 = 12

(vii) 60, 70, 420, 480

60 = 2² × 3 × 5

70 = 2 × 5 × 7

420 = 2² × 3 × 5 × 7

480 = 2⁵ × 3 × 5

HCF = 2 × 5 = 10

Question 2

Find HCF by Long Division Method

(i) 12, 20

20 ÷ 12 = 1 remainder 8

12 ÷ 8 = 1 remainder 4

8 ÷ 4 = 2 remainder 0

HCF = 4

(ii) 81, 117

117 ÷ 81 = remainder 36

81 ÷ 36 = remainder 9

36 ÷ 9 = remainder 0

HCF = 9

(iii) 935, 1320

1320 ÷ 935 = remainder 385

935 ÷ 385 = remainder 165

385 ÷ 165 = remainder 55

165 ÷ 55 = remainder 0

HCF = 55

(iv) 252, 576

576 ÷ 252 = remainder 72

252 ÷ 72 = remainder 36

72 ÷ 36 = remainder 0

HCF = 36

(v) 2241, 8217, 747

HCF (2241, 8217) = 249

HCF (249, 747) = 249

Answer = 249

(vi) 30, 120, 90, 210

HCF = 30

Question 3

What is the HCF of two prime numbers?

Two different prime numbers have only one common factor.

Answer = 1

Example:

HCF (7, 11) = 1

Conclusion

This chapter helps students understand factors, multiples, divisibility rules, prime numbers, composite numbers, and prime factorization. Mastering these concepts builds a strong foundation for higher mathematics and algebra.