Number Operations and Properties

Factors of 54 = 1, 2, 3, 6, 9, 13, 18, 27, 54 Factors of 100 = 1, 2, 4, 5, 10, 20, 25, 50, 100 Greatest common factor = 2 42 × 8 = 336 336 + 2 = 338

Multiples of 11 = 11, 22, 33, 44, 55, 66, 77, 88, 99, 110 Multiples of 10 = 10, 20, 30, 40, 50, 60, 70, 80, 90, 100, 110 Least common multiple = 110 Multiples of 12 = 12, 24, 36, 48, 60 Least common multiple of 12 and 10 = 60 110 + 60 = 170

Multiples of 6 = 6, 12, 18, 24, 30, 36, 42, 48, 54 Multiples of 18 = 18, 36, 54 Multiples of 27 = 27, 54 Least common multiple = 54 Fifth multiple of 5 = 7 × 5 = 35 54 - 35 = 19 so, 19 has 2 factors.

Factors of 64 are 1, 2, 4, 8, 16, 32, 64. Factors of 80 are 1, 2, 4 5, 8, 10, 16, 20, 40, 80. Greatest common factor of 64 and 80 is 16. Result obtained = 16 - 11 = 5

Greatest common factor of 36 and 30 is 6. Factors of 28 are 1, 2, 4, 7, 14, 28. Factors of 35 are 1, 5, 7, 35. G.C.F of 28 and 35 is 7. Result obtained = 6 + 7 = 13

The HCF of 56 and 72 is 8.

Factors of 6 = 1, 2, 3, 6 Factors of 18 = 1, 2, 3, 6, 9, 18 Greatest common factor = 6 6 × 4 = 24

Multiples of 8 = 8, 16, 24, 32, 40, 48 Multiples of 12 = 12, 24, 36, 48 Common multiples = 24, 48

Correct. Rs. 12

(n - 7) (n + 11) = n² + 11n - 7n - 77 (Using Foil) = n² + 4n - 77

(k + 13) (k - 7) = k² - 7k + 13k - 91 (Using Foil) = k² + 6k - 91

(3m + 5) (6n + 7) = 18mn + 21m + 30n + 35                     (Using Foil)

(n - 4) (n - 6) = n² - 6n - 4n + 24 (Using Foil) = n² - 10n + 24

(7k + 2) (12p + 5) = 84pk + 35k + 24p + 10                        (Using Foil)

(p - 5) (7p + 2) = 7p² + 2p - 35p - 10 (Using Foil) = 7p² - 33p - 10