The prime factorization of intezer N is A x A x B x C, where A, B and C are all distinct prine intezers. How many factors does N have?
To find the number of factors of ( N = A \times A \times B \times C ), where ( A ), ( B ), and ( C ) are distinct prime integers, we follow these steps:
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Prime Factorization in Exponent Form: Express ( N ) in exponent form as ( A^2 \times B^1 \times C^1 ).
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Calculate the Number of Factors: The formula to find the number of factors is to add 1 to each exponent and then multiply these numbers together. For ( N = A^2 \times B^1 \times C^1 ), the calculation is: [ (2 + 1) \times (1 + 1) \times (1 + 1) = 3 \times 2 \times 2 = 12 ]
Therefore, ( N ) has 12 factors.