Question

Grey said he is thinking of a mystery number. The number is between 20 and 30, and it has exactly 3 factors. What is Grey's mystery number?​

Answer 1

25

Explanation:

Let x be the mystery number.

The minimum number of factors a number can have is two:

• 1 and the number itself.

(These numbers are called prime numbers).

If a number has exactly 3 factors, it must be an perfect square number since every perfect square has an odd number of factors and any number that is not a perfect square will have an even number factors..

Odd square numbers between 20 and 30:

• 25

Factors of 25: 1, 5 and 25.

Therefore, Grey's mystery number is 25.

Proof:

• Factors of 20: 1, 2, 4, 5, 10 and 20.
• Factors of 21: 1, 3, 7 and 21.
• Factors of 22: 1, 2, 11 and 22.
• Factors of 23: 1 and 23. (23 is a prime number)
• Factors of 24: 1, 2, 3, 4, 6, 8, 12 and 24.
• Factors of 25: 1, 5 and 25.
• Factors of 26: 1, 2, 13 and 26.
• Factors of 27: 1, 3, 9 and 27.
• Factors of 28: 1, 2, 4, 7, 14 and 28.
• Factors of 29: 1 and 29. (29 is a prime number)
• Factors of 30: 1, 2, 3, 5, 6, 10, 15 and 30.