Multiples, factors and prime factors
In a nutshell
Every number is either a prime number, or a multiple of other factors.
Multiples, factors and primes
- Multiple - A multiple of a number is any number that can be formed as a product of that number and another number.
- Factor - A factor of a number is any number that divides the number with no remainder.
- Prime number - A prime number is a number which has only two distinct factors, 1 and itself.
Example 1
What are the factors of 36?
36=1×36
36=2×18
36=3×12
36=4×9
36=6×6
Hence the factors of 36 are 1,2,3,4,6,9,12,18,36.
Example 2
Is 162 a multiple of 27?
162÷27=6
Yes, 162 is a multiple of 27, as the quotient (6) is a whole number and there is no remainder.
Factor trees
You can find the prime factorisation of a number using a factor tree.
Procedure
- Write the number at the top and find two numbers which multiply to make the number.
- Write the pair of factors underneath the original number, "branching" them off to the left and right of the original number.
- If one, or both, of these factors are not prime, repeat this process until the end of every "branch" is a prime number.
- Write the numbers at the bottom of each branch, multiplied by one another. This is the prime factorisation.
Example 3
Use a factor tree to find the prime factorisation of 273.
273↙↘3◯91↙↘ 7◯13◯
Hence the prime factorisation of 273 is 273=3×7×13.
Note: If the original number is, itself, a prime number then you already have the number in its prime factorisation form.