Explain Prime Numbers vs. Composite Numbers?

Remember that when two or more numbers are multiplied together to make a certain number, these numbers are called factors of the given number. A prime number is a whole number that has only two factors: 1 and itself.

For example, 7 is a prime number, because 1 and 7 are its only factors.

The only exception to this definition is the number 1, which is NOT considered a prime number, even though it is only divisible by 1 and itself.

A composite number is a whole number that has more than 2 factors.

For example, 4 is a composite number because it has three factors: 1, 2, and 4.

Every whole number is either a prime number or a composite number, except for the numbers 0 and 1.

Prime Factorization

Factoring a number like 45 into prime numbers is called prime factorization.

Example: 45 = (3 x 3 x 5)

45 = 9 x 5 is a factorization, but it's not a "prime" factorization, because 9 is not prime.

Traditionally, factors are written in numerical order (smallest to largest).

The prime factorization for 45 is:

45 = (3 x 3 x 5)

Combining Prime Factors into Exponents

If you perform a prime factorization of a number like 45, the result can be presented in two different ways:

45 = (3 x 3 x 5)

or

45 = (3² x 5)