# What is the Factor?

## Factors

Factors are numbers that are multiplied together to obtain a product. For instance in 2 times 3 equals 6, 2 and 3 are the factors. Common factor a number that divides exactly into two or more other numbers.

For example, the factors of 12 are 1 times 12, 2 times 6 and 3 times 4. The factors of 12 are 1, 2, 3, 4, 6 and 12. The factors of 15 are 1 times 15, and 3 times 5. The factors of 15 are 1, 3, 5, and 15.

The common factors are 1 and 3. Those are the factors they have in common. Prime number. Prime numbers have two distinct, which means different, factors 1 and itself. The very first prime number is 2, because the only numbers the only factors of 2 are 1 and 2. 1 times 2 is 2.

Some people think that 1 would be the first prime number, but 1 only has one factor, 1. 1 times 1 is 1. 1 is commonly thought of as neither prime nor composite. A composite number being a number that has more than 2 factors.

2 would be the first prime number, then 3 because 3 has only two factors, 1 times three is 3. 4 would be composite since 1 times is 4 and also 2 times 2 is 4. 5 would be prime. It’s only factors are 1 and 5. 6 would be composite 1 times 6 is 6, and 2 times 3 is 6. 7 would be prime since it’s only factors are 1 and 7. 8 would be composite, 1 times 8 is 8, 2 times 4 is 8. 9 would also be composite, 1 times 9 is 9, 3 times 3 is 9. 10 would also be composite, 1 times 10 is 10, 2 times 5 is 10. 11 would be prime, 1 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. In our example above in 12 and 15 the prime factor of 12 would be 3 -2 and 3, and the prime factors of 15 would be 3 and 5. You can also do prime factorization. The prime factorization of a number, for instance the prime factorization of 12 would be 2 times 2 times 3.

That’s where you write the product of a number only using primes. The prime factorization of 15 would be 3 times 5. 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 product you are seeking.