# Prime Numbers

Prime number factors are numbers that are multiplied together to obtain a product. For instance, in two times three equals six, two and three are the factors.

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Common factor – a number that divides exactly into two or more other numbers, for example, the factors of 12 are one times 12, two times six and three times four.

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The following transcript is provided for your convenience.The factors of 12 are one, two, three, four, six and 12. The factors of 15 are one times 15 and three times five. The factors of 15 are one, three, five and 15. The common factors are one and three. Those are the factors they have in common.

Prime number – prime numbers have two distinct, which means different factors, one and itself. The very first prime number is two, because the only factors of two are one and two, and one times two is two. Some people, think that one would be the first prime number, but one only has one factor, one. One times one is one, so one is commonly thought of as neither nor composite.

A composite number being a number that has more than two factors, so two would be the first prime number, then three, because three has only two factors, one times three is three. Four would be composite, since one times four is four and also two times two is four. Five would be prime, its only factors are one and five. Six would be composite, one times six is six and two times three is six. Seven would be prime, since its only factors are one and seven. Eight would be composite, one times eight is eight, two times four is eight. Nine would also be composite, one times nine is nine, three times three is nine. 10 would also be composite, two times five is 10. 11 would be prime, one times 11 is 11 and so on and so forth.

There are an infinite number of primes. A prime factor is a factor that’s prime, so in our example above in 12 and 15, the prime factor of 12, would be two and three and the prime factors of 15, would be three and five. You can also do prime factorization, the prime factorization of a number, for instance, the prime factorization of twelve, would be two times two times three. That’s where you write the product of a number, only using primes and the prime factorization of 15 would be three times five, unlike just writing the factors of a number. With prime factorization, you use only prime numbers as factors to multiply to get the result of the prime product you are seeking.

Next Lesson: Greatest Common Factor