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Theoretically, infinity has an infinite number of factors. Since the number scale does not end you can't answer a question such as "What is the biggest number?" and therefore the number with the biggest number of factors is impossible to calculate unless you use a theoretical such as infinity.

More interestingly there is a debate about the largest prime number (a number with only two factors, 1 and itself) which may or may not be a finite number.

Also, 0 has infinite factors because it is divisible by every number.

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