# Group Theory – Understanding the role of Euler.

It must be a very basic and simple question related to euler's function. $$phi$$. If I wanted to calculate for example $$phi (100)$$ I saw that we can write it as $$phi (2 ^ 2 cdot 5 ^ 2)$$. I also saw a theorem that says $$phi (a cdot b) = phi (a) cdot phi (b)$$ Yes $$a, b$$ they are prime numbers. So we get $$phi (100) = phi (2) phi (2) phi (5) phi (5) = 1 cdot 1 cdot 4 cdot 4 = 16$$But it's not true because I know $$phi (100) = 40$$. What is the right why to dismantle? $$100$$ So can we use the euler function?