Higest Common Factor (HCF)

The Highest Common Factor (H.C.F) of two (or more) numbers is the largest number that divides evenly into both numbers.

In other words the H.C.F is the largest of all the common factors.

The common factors or of 12 and 18 are 1, 2, 3 and 6.
The largest common factor is 6, so this is the H.C.F. of 12 and 18.

It is very easy to find a H.C.F. of small numbers, like 6 and 9 (it is 3) or 8 and 4 (it is 4).
The best way is to keep finding the factors of the smaller number, starting from the largest factor. The first factor of the smaller number that is also a factor of the larger number is a H.C.F.

The H.C.F is useful when simplifying fractions.

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FINDING THE H.C.F. OF BIG NUMBERS

For larger numbers you can use the following method:

1. Find all prime factors of both numbers.
2. Write both numbers as a multiplication of prime numbers.
3. Find which factors are repeating in both numbers and multiply them to get H.C.F

Example:

Find the Highest Common Factor (H.C.F.) of 240 and 924.

Solution:

Finding all prime factors of 240:

We will start with the smallest prime number and we will divide 240 into it if we can come handy).
We will do the same with the result (or quotient), and we will keep dividing by prime numbers until we have 1 as a quotient.
Each time we write the prime factor to the right and the quotient below:

240	|	2	2 is a factor of 240;	240 divided by 2 is 120
120	|	2	2 is a factor of 120;	120 divided by 2 is 60
60	|	2	2 is a factor of 60;	60 divided by 2 is 30
30	|	2	2 is a factor of 30;	30 divided by 2 is 15
15	|	3	3 is a factor of 15;	15 divided by 3 is 5
5	|	5	5 is a factor of 5;	5 divided by 5 is 1
1

240 = 2 x 2 x 2 x 2 x 3 x 5

NOTE: There are other methods for finding all prime factors of a number, for example a factor tree.

Finding all prime factors of 924:

924	|	2	2 is a factor of 924;	924 divided by 2 is 462
462	|	2	2 is a factor of 462;	462 divided by 2 is 231
231	|	3	3 is a factor of 231;	213 divided by 3 is 77
77	|	7	7 is a factor of 77;	77 divided by 7 is 11
11	|	11	11 is a factor of 11;	11 divided by 11 is 1
1

924 = 2 x 2 x 3 x 7 x 11

Multiply the factors which repeat in both numbers to get the H.C.F.

The Highest Common Factor is 2 x 2 x 3 = 12

Example 2


Example 3