f(x) is defined as the largest integer n such that x is divisible by 2^n. Which of the following numbers is the biggest?
Choose the correct choice from the following
A) f(24)
B) f(42)
C) f(62)
D) f(76)
E) f(84)
So, we have an integer x. It has some power of 2 in its prime factorization (2^n) and f(x) is the value of that n. Basically f(x) is the power of 2 in prime factorization of x.   For example, if x is say 40, then f(x)=3. Why? Because the largest integer n such that 40 is divisible by 2^n is 3: 40/2^3=5, or 40=2^3*5 --&gt; the power of 2 in prime factorization of 40 is 3.   Hence all we need to do to answer the question is to factorize all options and see which one has 2 in highest power.   A. f(24) --&gt; 24 = 2^3*3   B. f(42) --&gt; 42 = 2*21   C. f(62) --&gt; 62 = 2*31   D. f(76) --&gt; 76 = 2^2*19   E. f(84) --&gt; 84 = 2^2*21   f(24)nswer: f(24).
<result>A</result>
f(x) is defined as the largest integer n such that x is divisible by 2^n. Which of the following numbers is the biggest?