Yes. For example, 52 ÷ 4 = 13.
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No. If you multiply two prime numbers, any prime numbers, the result will - by definition - not be a prime number. For example, if you multiply 2 x 3, the result will obviously be divisible by 2 and by 3, and therefore, not be a prime number. By the way, one is not usually considered a prime number.
No.
No.
There is no biggest prime number: they go on for ever.