If x is divisible by 42. Which of the following numbers is definitely a factor of x2? (Choose
all that apply.)
a) 63 b) 33 c) 36 d) 8
It will be helpful if group can explain the answer as well.
Given: \(x=42k=2*3*7*k\) (where \(k\) is an integer) --> \(x^2=2^2*3^3*7^2*k^2\).
A. \(63=3^2*7\) is a factor of \(x^2\);
B. \(33=3*11\) may NOT be a factor of \(x^2\) (we don't know whether 11 is a factor \(x^2\));
C. \(36=2^2*3^2\) is a factor of \(x^2\);
D. \(8=2^3\) may NOT be a factor of \(x^2\) (\(2^2=4\) is a factor of \(x^2\), but we need one more 2 and we don't know whether unknown multiple, \(k^2\), contains it or not).
Answer: A and C.