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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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8y ago
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8y ago

36 has 9 factors.

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Q: What is the largest two digit number to the exactly 9 factors?
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The best way to tackle this is to take the largest 3 digit number (999) and work out its prime factors. You can then work down until you get one with exactly five prime factors. 999 is 3x3x3x37, 998 is 2x499, 997 is prime, 996 is 2x2x3x83, 995 is 5x199, 994 is 2x7x71, 993 is 3x331, 992 is 2x2x2x2x2x31, 991 is prime, 990 is 2x3x3x5x11. That is the first we came across with five prime factors. Therefore the largest 3 digit number with exactly five prime factors is 990.


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