We know that a factor is a quantity which divides the given quantity without leaving any remainder. Similar to LCM above we can find a highest common factor (HCF) of the given numbers. Let us look at its definition first. The highest common factor is a quantity obtained from the given quantities and which divides each of them without leaving a remainder. We understand this by taking an example.
Example
Find the HCF of 49 and 63.
The factors of 49 are 1, 7 and itself. The factors of 63 are 1, 3, 7, 9, 21 and itself. The common factors are 1 and 7. The highest of these is 7, which is the HCF we require.
This is one of the methods to obtain the HCF. This method may prove tedious if we are given bigger numbers and more of them. When such quantities are given, we follow division method as shown below (this method is shown for numbers in the above example).
In this method the first step constitutes dividing the larger quantity by the smaller quantity and subtract it as shown to obtain a remainder (it is not necessary that we ought to get a remainder in all the cases). Then the divisor, 49 (in our case, 49 is the divisor and 63 the dividend, 1 the quotient and 14, the remainder) becomes the dividend and the remainder (14) which we obtained earlier becomes the divisor. We continue doing this until the remainder is 0 as shown below. The last divisor is our HCF.
49) 63 (1
49
---------
14) 49 (3
42
--------
7) 14 (2
14
-----
0
That is, 7 is the HCF of the numbers 49 and 63.
Now let us consider three quantities and obtain the HCF for them.