3, 5 and 7
4, 9, 25 and 49.
All nonzero numbers have factors. Some numbers have some of the same factors as other numbers. These are known as common factors. 3 is a common factor of 9 and 12.
Yes. Composite numbers have more than exactly two factors; 39 has four factors: 1, 3, 13, 39. Prime numbers have exactly two factors, eg 3 has the two factors 1 and 3. Square numbers have an odd number of factors, eg 36 has nine factors: 1, 2, 3, 4, 6, 9, 12, 18, 36. The number 1 is not prime as it only has one factor: 1.
Numbers with exactly 6 factors are perfect squares of prime numbers. The prime factorization of a number with exactly 6 factors is in the form ( p^2 ), where ( p ) is a prime number. There are 10 prime numbers less than 30: 2, 3, 5, 7, 11, 13, 17, 19, 23, and 29. So, there are 10 numbers less than 30 that have exactly 6 factors.
All numbers that are the square of primes have exactly 3 factors.
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
4 and 9
Prime squares have three factors. 4, 9, 25
2 4 6