The question for the day is a question on factors/divisors of a number in the topic number theory.
Question
If both 112 and 33 are factors of the number a * 43 * 62 * 1311, then what is the smallest possible value of a?
A. 121
B. 3267
C. 363
D. 33
E. None of the above
The correct choice is (C) and the correct answer is 363.
Explanatory Answer
112 is a factor of the given number. The number does not have a power or multiple of 11 as its factor. Hence, "a" should include 112
33 is a factor of the given number. 62 is a part of the number. 62 has 32 in it. Therefore, if 33 has to be a factor of the given number a * 43 * 62 * 1311, then we will need at least another 3.
Therefore, "a" should be at least 112 * 3 = 363 if the given number has to have 112 and 33 as its factors.
The smallest value that "a" can consequently take is 363.
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