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Can We Have a Number Which Has an Infinite Number of Factors?

Published in Number Theory 1 min read

Yes, the number 0 has an infinite number of factors.

Here's why:

Any number that divides evenly into another number is considered a factor of that number. For any non-zero number n, 0 can be expressed as n 0 = 0. This means any number n* is a factor of 0.

Therefore, every integer (positive, negative, and zero) is a factor of 0. Since there are an infinite number of integers, 0 has an infinite number of factors.

It's important to note that while 0 has an infinite number of factors, it is not a factor of any non-zero number. Division by zero is undefined.

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