If both 112 and 33 are factors of the number a × 43 × 62 × 1311, then what is the smallest possible value of 'a'?

Question: If both 112 and 33 are factors of the number a × 43 × 62 × 1311, then what is the smallest possible value of 'a'?Solution:a × 43 × 62 × 1311 can be expressed in terms of its prime factors as a × 28 × 32 × 1311112 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 be a part of '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 question is "what is the smallest possible value of 'a'?"The smallest value that 'a' can take is 363