Highest common factor
What is the highest common factor?
Section titled “What is the highest common factor?”The HCF (highest common factor) of numbers is the largest factor that goes into both/all numbers.
For example, the HCF of
Finding the highest common factor
Section titled “Finding the highest common factor”To find the highest common factor, you need to be familiar with prime factor decomposition.
Here are the steps:
- Find the prime factor decomposition of each number.
- Find the common prime factors (and how many of each there are)
- Multiply the common prime factors together to get the HCF
Example: Find the HCF of
Section titled “Example: Find the HCF of and .”- Find the prime factor decomposition of each number:
- Find the common prime factors:
- Both have at least
as a factor - Both have at least
as a factor
- Both have at least
- Multiply the common prime factors together:
Answer:
Example: Find the HCF of
Section titled “Example: Find the HCF of , and .”- Find the prime factor decomposition of each number:
- Find the common prime factors:
- All have at least
as a factor - All have at least
as a factor
- All have at least
- Multiply the common prime factors together:
Answer:
Uses of the highest common factor
Section titled “Uses of the highest common factor”We can use the HCF to:
- simplify fractions
- divide things up more easily
- simplify ratios
- (and more)