Question

find the hcf of 625,1125and2125 using Euclid's division lemma.

Answer 1

Prime factorisation of these numbers are: 
(1) 625= 5×5×5×5 = 5^4 
(2)1125=3×3×5×5×5= 3^2 × 5^3 
(3)2125= 5×5×5×17 = 5^3×17 
Now, HCF = product of smallest power of each common prime. 
hence, HCF(625,1125,2125) is 5^3 or 125

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