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Q: What number less than ninety has the greatest number of factors?

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12

48

The three greatest whole numbers less than 200 that each have an odd number of factors are 144, 169 and 196.

60, 72, 84, 90 and 96 each have twelve factors.

60, 72, 84, 90 and 96 each have twelve factors.

The greatest possible 'length' comes from the number with the greatest number of prime factors. The greatest number of factors is created by using the smallest prime number, 2, as a factor as many times as possible. Since 2^9=512 and 2^10=1024, the greatest possible 'length' of a positive integer less than 1000 is 9.

greatest number less then 100 = 99

60, 72, 84, 90 and 96 are tied with 12.

The greatest composite number that is less than 100 is 99. Its factors are 1, 3, 9, 11, 33, and 99. It can't be prime because it has factors other than 1 and itself.

Mercury and Venus.

Short answer: There is none. There are not common factors of a single number because there cannot be any form of common factor without two or more numbers to compare. Common factors are factors that the numbers being compared have in common. Thus, there cannot be a single number that has the greatest number of common factors.

What is the greatest palindromic number less than 999?

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