works for me by int

1. int segments = 360;
2. int radius = 300;
3. void setup() {
4.   size(800, 800);
5.   colorMode(HSB, 360, 100, 100);
6.   noStroke();
7.   // smooth();
8. }
9. void draw() {
10.   background(360);
11.   float segments = map(mouseX, 0, width, 3, 360);
12.   int segments2  =  int (segments);
13.   if ((360%segments2)!=0) {
14.     println ("oups");
15.   }
16.   else
17.   {
18.     println ("right -----------");
19.   }
20.   // get something that is good for making exact 360
21.   // ?
22.   float angleStep = 360f/segments2;
23.   //angleStep+=1;
24.   beginShape(TRIANGLE_FAN);
25.   vertex(width/2, height/2);
26.   for (float angle = 0; angle <= 361; angle += angleStep) {
27.     float vx = width/2 + cos(radians(angle))*radius;
28.     float vy = height/2 + sin(radians(angle))*radius; 
29.     vertex(vx, vy);
30.     fill(angle, 100, 100);
31.   }
32.   endShape();
33. }

new version:
in a while loop it goes to the first number with 360 modulo (it's expressed by % in processing) this number
is = 0

Looks beautiful by the way  

1. int segments = 360;
2. int radius = 300;
3. void setup() {
4.   size(800, 800);
5.   colorMode(HSB, 360, 100, 100);
6.   noStroke();
7.   // smooth();
8. }
9. void draw() {
10.   background(360);
11.   float segments = map(mouseX, 0, width, 1, 360);
12.   int segments2  =  int (segments);
13.   while ( (360 % segments2)!=0)
14.     segments2++;
15.   if ((360%segments2)!=0) {
16.     println ("oups");
17.   }
18.   else
19.   {
20.     println ("right -----------"+segments2);
21.   }
22.   // get something that is good for making exact 360
23.   // ?
24.   float angleStep = 360f/segments2;
25.   //angleStep+=1;
26.   beginShape(TRIANGLE_FAN);
27.   vertex(width/2, height/2);
28.   for (float angle = 0; angle <= 360; angle += angleStep) {
29.     float vx = width/2 + cos(radians(angle))*radius;
30.     float vy = height/2 + sin(radians(angle))*radius; 
31.     vertex(vx, vy);
32.     fill(angle, 100, 100);
33.   }
34.   endShape();
35. }

thanks that helped

there must be a formula

but it works without the while

the important part was:

1.   int segments2  =  int (segments);