A positive integer can be expressed as the product of its factors. A factor is simply a number that is multiplied to get a product.

Factoring is like taking a number apart. Factoring a number means taking the number apart to find its factors. It's like multiplying in reverse.

Here are some of examples.
• 1 (1 × 1) ⇒ 1
• 5 (1 × 5) ⇒ 1, 5
• 6 (1 × 6), (2 × 3)⇒ 1, 2, 3, 6
• 7 (1 × 7) ⇒ 1, 7
• 16 (1 × 16), (2 × 8), (4 × 4) ⇒ 1, 2, 4, 8, 16
• 20 (1 × 20), (2 × 10), (4 × 5) ⇒ 1, 2, 4, 5, 10, 20

A prime number is any of the positive numbers that has exactly two factors, one and itself. Below are all the prime numbers within 100:

2,3,5,7,11,13,17,19,23,29,31,37,41,43,47,53,59,61,67,71,73,79,83,89,97

A composite number is any number that has more than two factors. All the positive numbers that is not a prime is a composite number except 1 (1 is neither a prime nor a composite numbers!)

Prime factor(s) of positive integers
• 1 has no prime factor
• Any prime number has exactly one prime factor, itself
• Any composite number can be written as a product of prime factors. This is called prime factorization.

  To find the prime factors of a number, you divide the number by the smallest possible prime number and work up the list of prime numbers until the result is itself a prime number.

  Example to find the prime factors of 12.
  • Since 12 is even, we start by dividing it by the smallest prime number, 2. 12 ÷ 2 = 6.
  • 6 is still an even number, 6 ÷ 2 = 3.
  • 3 is prime, so we are done finding all the prime factors of 12, they are: 2, 2, and 3. Or you can write down as 12 = 2² × 3. How many factors does 12 have? (1,2,3,4,6,12) (2 + 1)(1 + 1) = 6
  • Another example, the prime factors of 90: 90 = 2 × 3² × 5. How many factors does 90 have? (1,2,3,5,6,9,10,15,18,30,45,90) (1 + 1)(2 + 1)(1 + 1) = 12.

The greatest common factor of two positive integers, or GCF, is the greatest factor that divides the two numbers. To find the GCF of two numbers:
• List the prime factors of each number.
• Multiply those factors both numbers have in common to get the GCF
• If there are no common prime factors, the GCF is 1.
• Example: GCF of 12 and 20
  • The prime factors of 12: 2, 2, 3
  • The prime factors of 20: 2, 2, 5
  • The common factors are 2 and 2, their product is (2 × 2) = 4 is the GCF of 12 and 20.
• Example: GCF of 12 and 8
  • The prime factors of 12: 2, 2, 3
  • The prime factors of 8: 2, 2, 2
  • The common factors are 2 and 2, their product is (2 × 2) = 4 is the GCF of 12 and 8.
• Example: GCF of 4 and 8
  • The prime factors of 4: 2, 2
  • The prime factors of 8: 2, 2, 2
  • The common factors are 2 and 2, their product is (2 × 2) = 4 is the GCF of 4 and 8.