If N is the smallest positive integer that is not prime and does not divide 30!. How many factors does N have?
Explanation:
30! is divisible by all prime numbers less than 30.
∴ The smallest prime number that is not its factor is 31.
But N should not be a prime factor. ∴ N must be kept as small as possible i.e., 31 × 2 = 62.
The factors of 62 are 1, 2, 31 and 62, i.e., 4.
Hence, 4.
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