Prime Factor Decomposition (CIE IGCSE Maths: Core)

What are prime factors?

• A factor of a given number is a value that divides the given number exactly, with no remainder
  
  • e.g. 6 is a factor of 18
• A prime number is a number which has exactly two factors; itself and 1
  
  • e.g. 5 is a prime number, as its only factors are 5 and 1
  • You should remember the first few prime numbers:
    • 2, 3, 5, 7, 11, 13, 17, 19, …
• The prime factors of a number are therefore all the primes which multiply to give that number
  • e.g. The prime factors of 30 are 2, 3, and 5
    • 2 × 3 × 5 = 30

How do I find prime factors?

• Use a factor tree to find prime factors
  • Split the number up into a pair of factors
  • Then split each of those factors up into another pair
  • Continue splitting up factors along each "branch" until you get to a prime number
    • These can not be split into anything other than 1 and themselves
    • It helps to circle the prime numbers at the end of the branches

• A number can be uniquely written as a product of prime factors
  • Write the prime factors as a multiplication, in ascending order
    • 360 = 2 × 2 × 2 × 3 × 3 × 5
  • This can then be written more concisely using powers
    • 360 = 2³ × 3² × 5
• A question asking you to do this will usually be phrased as "Express … as the product of its prime factors"