A factor of a integer is an integer that divides the second integer into a third integer exactly; i.e. A is a factor of B if B/A is exactly C, where all of A, B and C are integers. A prime factor is a factor as above, but is also a Prime number. This means that the only factors of that factor are one and the number itself; i.e. A is a prime factor of B if B/A is exactly C andthe only factors of A are 1 and A.
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All numbers have factors. Some factors are prime numbers. These are known as prime factors. The set of prime factors is a subset of the set of factors for any given number.
The difference is that a prime number only has two factors that's one and itself, a composite has more factors than one and itself.
A prime factorization is a multiplication sentence of prime factors. 2, 3 and 5 are the prime factors of 30. 2 x 3 x 5 is the prime factorization of 30.
A factor string consists of any factors (except 1) that multiply to equal the number. Prime factorization consists of only prime numbers that multiply to equal the number. In the case where the factors of the original number consists only of primes, there is no difference.
The prime factors of 30 are 2, 3 and 5. The prime factors of 40 are 2 and 5. The prime numbers between 30 and 40 are 31 and 37.