If m is a positive integer and m^2 is divisible by 48, then the largest positive integer that must divide m is?
(A) 3
(B) 6
(C) 8
(D) 12
(E) 16
Is there a strategic approach to this question? Can any experts help?
Hi ardz24,
Let's take a look at your question.
The question states:
"If m is a positive integer and m^2 is divisible by 48, then the largest positive integer that must divide m is? "
The largest positive integer that must divide m will be m itself.
One way to solve this question is to check each of the option if it is true or not.
For that purpose, square each of the given options and find out if it is divisible by 48 or not.
Let's start from
option A.
Let m = 3 then m^2 = 9
9 is not divisible by 48 because it is less than 48.
Option B
Let m = 6 then m^2 = 36
36 is not divisible by 48 because it is less than 48.
Option C
Let m = 8 then m^2 = 64
64 is not divisible by 48 because it gives a decimal quotient when we try to divide 64 by 48.
Option D
Let m = 12 then m^2 = 144
144 is divisible by 48 because 144/48 = 3
Hence, the largest positive integer that must divide m is 12.
Therefore, Option
D is correct.
Hope it helps.
I am available if you'd like any follow up.
