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# Sunday Afternoon Maths LVII

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Posted on 2016-11-27

## Square Factorials

Source: Woody at Maths Jam
Multiply together the first 100 factorials:
$$1!\times2!\times3!\times...\times100!$$
Find a number, $$n$$, such that dividing this product by $$n!$$ produces a square number.

## Largest Odd Factors

Pick a number. Call it $$n$$. Write down all the numbers from $$n+1$$ to $$2n$$ (inclusive). For example, if you picked 7, you would write:
$$8,9,10,11,12,13,14$$
Below each number, write down its largest odd factor. Add these factors up. What is the result? Why?
If you enjoyed these puzzles, check out Sunday Afternoon Maths LXI,
puzzles about factors, or a random puzzle.