Question 1

Let $$1+\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+\frac{1}{5}+\frac{1}{6}=\frac{m}{n}$$, where $$m$$ and $$n$$ are positive integers with no common divisors other than $$1$$. The highest power of $$7$$ that divides $$m$$ is

Solution

Using denominator $$60$$, the sum is $$\frac{60+30+20+15+12+10}{60}=\frac{147}{60}=\frac{49}{20}$$. Thus $$m=49=7^2$$. Therefore, the highest power of $$7$$ dividing $$m$$ is $$2$$.

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Let $$1+\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+\frac{1}{5}+\frac{1}{6}=\frac{m}{n}$$, where $$m$$ and $$n$$ are positive integers with no common divisors other than $$1$$. The highest power of $$7$$ that divides $$m$$ is

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