If n is a positive integer and n^2 is divisible by 72, then the largest positive integer that must divide n is A. 6 B. 12 C. 24 D. 36 E. 48
Dear Expert,
need great help. I still cant understand after spending time on the solution.
If n is a positive integer and n^2 is divisible by 72, then the largest positive integer that must divide n is A. 6 B. 12 C. 24 D. 36 E. 48
From the statement, it says:
n^2 = 72k
n^2 = 36 x 2k
n = 6 x square root of 2k
From here , the minimum value of k = 2, hence the value of n = 12
but I can also take other value if I use this equation. eg n = 48
n^2 = 72k
n= 6 x square root of 2k
n = 6 x square root of 2(32)
n = 6 x 8
n = 48
Hope to hear from you. Many thanks
The key thing here is to save time. As you have seen the question can be easily solved.
Here,
72 = 2^3
(n^2)/(2^3 x 3^2) = Integer, as n-squared is perfectly divisible.
So, the least values of n that can be perfectly divisible is s
n/(2^2 x 3) i.e. n/12.
Hence, the answer is 12.