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?