How scaling actually behaves
Linear, the easy ones
Flour, sugar, milk, water, and the fats like butter and oil all scale one to one with your factor. Multiply and move on.
Leavening, the trap
Baking powder, baking soda, and yeast are where scaling bites. Push them up at full strength and a large batch can dome, then sink, or turn soapy. One common fix scales them by the square root of the conversion factor to hold back the rise. That square root move is a baker's rule of thumb, not a chemistry law, and it still shifts with altitude and humidity. Another common guideline just trims leavening back once you reach a double batch or more.
Salt and strong spice
Salt behaves the same way. Bring it below the straight line amount first, then taste and raise it. Strong, hot spices like cayenne and dried chili start lighter still and get adjusted once the batch is together, because heat compounds in a big pot.
Bake time does not ride along
A smaller batch can be done well before you expect, so read it by doneness, not by the clock times your factor. For a deeper or fuller pan, drop the oven a little and give it more time.
A large egg out of the shell runs about 50 grams, its white about 35 grams, its yolk about 14 grams, so half an egg is easy to weigh. Crack, whisk, and use half the weight when a scaled recipe lands on something like 1.5 eggs.