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Prime Factor Decomposition
➢ What are prime factors?
• Factors are things that are multiplied together.
• Prime numbers are numbers which have exactly two factors:
o Themselves and 1
• The prime factors of a number are therefore all the prime numbers
which multiply to give that number.
• You should remember the first few prime numbers:
o 2, 3, 5, 7, 11, 13, 17, 19, …
➢ How do I find the prime factors?
• Use a FACTOR TREE to find prime factors:
o Split a number up into a pair of factors which multiply to give
the number.
o Continue splitting up numbers until you get to a prime number
• These cannot be split into anything other than 1 and themselves.
• A number can be uniquely written as a product of prime factors:
o Write the prime factors in ascending order with “×” between,
▪ e.g. 504 = 2 × 2 × 2 × 3 × 3 × 7
Write with powers, so;
▪ 504 = 23 × 32 × 7
Example:
➢ Find the prime factors of 360. Give your answer in the form 2p ×
2q × 5r, where “p, q and r” are integers to be found.
For each number find any two numbers (not 1), which are factors and write
those as the next pair of numbers in the tree. If a number is prime, put a
circle around it. When all the end numbers are circled, you are done.
