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
Answers
Answered by
3
(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
Similar questions