1 = 44 ÷ 44

2=sqrt 4 - (4 - 4) x 4

3 = (4 + 4 + 4) ÷ 4

4 = 4 + 4 × (4 - 4)

... ...

7= 44/4-4

... ...

19=4!-4-4/4

... ...

100=4*4!+sqrt(4*4)

etc

Allow use of concatenation, +, -, x, /, sqrt, exponentation, factorial,decimal fractions, overline & brackets.

Source: Inspired by Martin Gardner statement.