The factors of 30 are 1, 2, 3, 5, 6, 10, 15 and 30. A number is considered the factor of another number when it can be evenly divided into that number.
If the only factors for a number are 1 and the number itself, it is considered a prime number. Common factors between two numbers are any factors shared by both of those numbers. The greatest common factor is the biggest of those common factors. There are multiple ways to find the greatest common factor, one of which is to list all the factors of both numbers. Another method is finding the shared prime number factors and multiplying them together. The greatest common factor is useful for simplifying fractions, because dividing the numerator and the denominator by the greatest common factor simplifies the fraction as low as possible.
Numbers can be broken down into prime number factors through prime factorization, also known as integer factorization. This is done by continually breaking down a number into smaller factors until the only factors left are prime numbers. Prime factorization can be very difficult and complex for larger numbers, and no method is known to complete long factorizations quickly as of 2014.