What numbers under 100 have 12 factors?

Answer 1

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 ).

Answer 2

60, 72, 84, 90 and 96