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All numbers that are the square of primes have exactly 3 factors.

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Squares of prime numbers.

Q: What numbers have exactly 3 factors?

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Numbers with exactly three factors are squares of prime numbers.

The squares of all prime numbers above 2 have exactly 3 factors.

Numbers with three factors are squares of primes. So: 4, 9, 25

11

The way to be sure you have one of these is to take any three distinct prime numbers and multiply them. Those three prime numbers are then the only factors the product can have. An example is the number 30, which has factors of 2, 3 and 5.

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Squares of prime numbers have exactly three factors.

Numbers with exactly three factors are squares of prime numbers.

The squares of all prime numbers above 2 have exactly 3 factors.

By definition, a prime number has exactly two factors. So, there are no prime numbers with exactly three factors.

Prime squares

A number has exactly three factors if and only if it is the square of a prime number.

2 and 3

3, 5 and 7

Prime numbers have exactly two factors. 3 has exactly two factors: 1 and 3. So 3 is prime. Composite numbers have more than two factors. 4 is composite because it has three factors: 1, 2, and 4.

4 and 9

Prime squares have three factors. 4, 9, 25

2 4 6