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That has a name. Ask a model to work through something step by step instead of answering straight away, and the written sequence it produces is called a chain of thought. For some models and some tasks it measurably improves the answer.
Long division is the same trick. The figures you write down hold the intermediate results, so you do not have to keep them in your head. The model has no head to keep them in at all, so writing a step down is the only way it still has that step when it picks the next token.
Which makes asking for the steps good advice, and also weaker than it sounds.
More words mean more places for something to go wrong. A model that reasons carefully to a wrong answer has produced a longer wrong answer, and it will look more convincing than the short one.
And the steps are not a report of how the answer was reached. Researchers have fed models questions with a hidden nudge in them, something that quietly pushed towards one answer, and found the models following the nudge while explaining their reasoning without ever mentioning it. The explanation was fluent, plausible, and not what happened.
So read the steps as a claim you can check rather than as a window into the machine. A chain you verify is worth something. A chain that merely sounds right is worth what it sounds like.