Because 1 is the only positive integer that divides evenly into 1 with no remainder.
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No prime number only has one factor. Each prime number has itself and 1 as factors. Now, the number 1 of course has only one factor, but it is technically not a prime number.
1 has 1 factor.
103 is a prime number. The only two factors of a prime number are 1 and itself. The only factor pair of 103 is 1 x 103. There is only one factor pair of a prime number. The proper factors of 103 are only 1 or, if the definition you are using excludes 1, there are none. The only prime factor of 103 is 103. There is only one prime factor of a prime number - itself. The distinct prime factor (listing each prime factor only once) of 103 is also 103.
The factor pair for 31 is 1*31. Since 31 is prime, it has only one factor pair.
The factor pairs of 29 are 1 and 29. 29 is prime so it has only one factor pair.