Highest common factor, also called HCF, is the largest number which can be divided by both of two given numbers without remainder. This number is the greatest common divisor of two numbers.
To understand the concept of highest common factor, let us start with a simple example. Suppose we want to find the highest common factor of 6 and 8. We can first notice that 6 cannot be divided by 8 because 8 is a multiple of 2 and 2 is the smallest number which can be divided by 6 without remainder. So, the highest common factor of 6 and 8 is 2.
Now, suppose we want to find the highest common factor of 4 and 5. We can notice that 4 cannot be divided by 5 without remainder. Therefore, the highest common factor of 4 and 5 is 1.
 | = | least common multiple |
 | = | greatest common divisor |
 | = | non-zero integers |