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02/02/2024 · Junior High School
Which of the nurbbers below have exactly three divisors?
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A number has exactly three divisors if and only if it is the square of a prime number. This is because the divisors of a number \( n = p^2 \) (where \( p \) is a prime) are \( 1, p, \) and \( p^2 \), which gives us exactly three divisors.
To find numbers with exactly three divisors, you can look for perfect squares of prime numbers. For example:
- \( 2^2 = 4 \) (divisors: 1, 2, 4)
- \( 3^2 = 9 \) (divisors: 1, 3, 9)
- \( 5^2 = 25 \) (divisors: 1, 5, 25)
- \( 7^2 = 49 \) (divisors: 1, 7, 49)
- \( 11^2 = 121 \) (divisors: 1, 11, 121)
If you have a specific list of numbers you would like to check, please provide them, and I can help identify which of those have exactly three divisors.
Quick Answer
Numbers with exactly three divisors are perfect squares of prime numbers, such as 4, 9, 25, 49, and 121.
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