SOLUTION: What is the smallest possible value for a so that the number N = 3 x 7^3 x a is a multiple of 66?

Question 839186: What is the smallest possible value for a so that the number N = 3 x 7^3 x a is a multiple of 66?
Answer by fcabanski(1391) (Show Source): You can put this solution on YOUR website!
The prime factors of N are 7,7,7,3. a is the final factor of N. a may or may not be prime.

The prime factors of 66 are 3, 11. and 2

For N to be a multiple of 66, it must share prime factors with 66. N has 3 in common with 66, but is missing 2 and 11. a has to be a multiple of those missing factors. So a is not prime. The smallest a is 2*11 = 22.

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