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1 only has one factor, which is 1. Therefor it is neither prime or composite.
A factor is a number or quantity that when multiplied with another produces a given number or expression. Some factors are prime, some are composite (the number "1" is neither.) A composite factor is a factor that can be divided further. 8 is a composite factor of 24. 3 is a prime factor of 24.
A composite factor is a factor that is a composite number, as opposed to a prime factor which is a factor that is a prime number.
4 is a factor of 36, but it is not a prime number.
25 is a composite number. A prime number has only 2 factors which are 1 and itself. Composite numbers are everything else except 1 and 0. 1 and 0 are neither prime, nor composite.