Question 20

The smallest perfect square that is divisible by 7!

Solution

7! can be broken into prime factors.

7! = 1*2*3*4*5*6*7 = $$2^4*3^2*5*7$$

Hence, the smallest perfect square which is divisible by 7! will $$2^4*3^2*5^2*7^2$$ = 5040*5*7 = 176400

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