Any product of 2 prime numbers will have 4 factors. Any Prime number to the 3rd power will have 4 factors.
6, 8, 10, 14, 15, 21, 22, 26, 27, 33, 34, 35, 38, 39, 46, 51, 55, 57, 58, 62, 65, 69, 74, 77, 82, 85, 86, 87, 91, 93, 94, 95
Numbers under 100 that have 12 factors must be in the form of ( p_1^{11} ) or ( p_1^3 \times p_2^2 ), where ( p_1 ) and ( p_2 ) are distinct prime numbers. The prime factorization of 12 is ( 2^2 \times 3 ). Thus, the numbers under 100 with exactly 12 factors are ( 2^{11} = 2048 ) and ( 2^3 \times 3 = 24 ).
6 (1,2,3,6) 10 (1,2,5,10) and 15 (1,3,5,15).
There are exactly 50 even numbers if you include 100. There are exactly 50 odd numbers if you include 1.
24edit: nonethe smallest number with 12 distinct factors would be2*3*5*7*11*13*17*19*23*29*31*37>>100
4, 9, 25, and 49 are all of the numbers between 1 and 100 having 3 factors.
There are five numbers in that range with 12 factors, but none with exactly eleven.
16 and 81 are the only two.
By definition, a prime number has exactly two factors. So, there are no prime numbers with exactly three factors.
Each of the 25 prime numbers from 1 to 100 has exactly two factors, 1 and the number itself. The other 75 numbers from 1 to 100 are not prime numbers because none of them have exactly two factors.
4 (4,2,1) 9 (9,3,1) 25 (25,5,1) 49 (49,7,1) i think that is it...
Numbers under 100 that have 12 factors must be in the form of ( p_1^{11} ) or ( p_1^3 \times p_2^2 ), where ( p_1 ) and ( p_2 ) are distinct prime numbers. The prime factorization of 12 is ( 2^2 \times 3 ). Thus, the numbers under 100 with exactly 12 factors are ( 2^{11} = 2048 ) and ( 2^3 \times 3 = 24 ).
There are a lot more than three! 6 (1,2,3,6) 10 (1,2,5,10) 15 (1,3,5,15)
No numbers between 1 and 100 have exactly eleven factors. 60, 72, 84, 90 and 96 each have twelve factors.
4, 9, 25 and 49.
In that range, only 100 has exactly 9 factors.
Numbers having exactly three factors are the squares of prime numbers. Examples of these numbers greater than 100 are 121, 169, 289, 361, 529, 841, etc.
Just 36.