Question

10. Find the greatest number that will divide
(a) 61,94 and 140 leaving 1,4 and 5 respectively
(b) 69, 117 and 149 leaving 5 in every case​

Answer 1

(a) Clearly, the required no. divides (61-1)=60, (94-4)=90, (140-5)=135 completely.

60 = 2×2×3×5 = 2²×3×5

90 = 2×3×3×5 = 2×3²×5

135 = 3×3×3×5 = 3³×5

HCF = lowest power of common factors = 3×5 = 15

required no. = 15

(b) Clearly the required no. divides (69-5)=64, (117-5)=112, (149-5)=144 completely.

64 = 2×2×2×2×2×2 = 2^6

112 = 2×2×2×2×7 = 2⁴×7

144 = 2×2×2×2×3×3 = 2⁴×3²

HCF = lowest power of common factors = 2⁴ = 16