Question 4 the day : June 22, 2005

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?

1. 121
2. 3267
3. 363
4. 33

Correct choice (3). Correct Answer - (363)

Explanatory Answers

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, if "a" should be at least 11² * 3 = 363 if the given number has to have 11² and 3³ as its factors.

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