To have exactly 9 factors, the number would either have to have a Prime number raised to the 8th. power; this is not possible with two digits.The other option is to have a prime number raised to the second power, times another prime number raised to the second power. (The number of factors in this case is (2 + 1)(2 + 1).) This is only possible if you use the prime factors 2 and 3; any other combination of prime numbers will yield a number that has more than 2 digits.
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The largest one digit number that has three factors is 9. Its factors are 1, 3, and 9.
Oh, dude, the largest two-digit number with exactly 7 factors is 48. Yeah, it's like a hidden gem in the world of numbers. It's got 1, 2, 3, 4, 6, 8, and 12 as factors, making it the cool kid with just the right amount of friends.
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If factors include 1 and the number itself then the any number (n) with only 4 factors has to be the product of two prime numbers, p1 and p2. The factors are then n, p1, p2, and 1. The largest 3-digit number with only 4 factors is 998. The factors are 998, 499, 2 and 1