If a circle is provided with a measure of 19° on centre, is it possible to divide the circle into 360 equal parts

Question

I thought like 19 degree is the central angle and complete angle of circle is 360 degree.

So,i divide 360/19 get approx 19 sectors.

But they are asking dividing the circle 360 equal parts. what i am doing wrong and how it should be comprehend correctly because i guess i am comprehending the question wrong way.

Answer 1

Hint: $19^2=361$.${}{}{}{}{}{}{}{}$

Answer 2

If you just go round the circle in steps of $19^\circ$, then after $360$ steps you will have visited all the multiples of $1^\circ$. (This is because $19$ and $360$ are coprime.)