Question : If the HCF of 45 and 55 is expressible in the form of 55 × 5 + 45m, then what is the value of m?
Option 1: –6
Option 2: 5
Option 3: 6
Option 4: –5
Correct Answer: –6
Solution : HCF of 45 and 55 = 5 5 = 55 × 5 + 4m ⇒ 5 = 275 + 45m ⇒ 5 – 275 = 45m ⇒ – 270 = 45m $\therefore$ m $=\frac{-270}{45}=-6$ Hence, the correct answer is $-6$.
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