If both 112 and 33 are factors of the number a * 43 * 62 * 1311, then what is the smallest possible value of a? Pick one.
A) 121
B) 3267
C) 363
D) 33
E) None of the above
Explanatory Answer   Step 1: Prime factorize the given expression   a * 43 * 62 * 1311 can be expressed in terms of its prime factors as a * 28 * 32 * 1311   Step 2: Find factors missing after excluding 'a' to make the number divisible by both 112 and 33   112 is a factor of the given number.   If we do not include 'a', 11 is not a prime factor of the given number.   If 112 is a factor of the number, 112 should have been in 'a'   33 is a factor of the given number.   If we do not include 'a', the number has only 32 in it.   Therefore, if 33 has to be a factor of the given number 'a' has to contain 31 in it.   Therefore, 'a' should be at least 112 * 3 = 363 if the given number has 112 and 33 as its factors.   The smallest value that "a" can take is 363.   363hoice 363 is the correct answer.
<result>C</result>
If both 112 and 33 are factors of the number a * 43 * 62 * 1311, then what is the smallest possible value of a?