## Highest Common Factor (HCF) | How To Find HCF Of Numbers

The full form of HCF is the Highest Common Factor. HCF can be useful in solving many mathematical problems. In many competitive exams questions related to HCF are asked. It is different from LCM. The LCM is found by multiplying all the factors which appear in either list whereas HCF is found by multiplying as ll the factors which appear in both lists.

### Highest Common Factor

Highest Common Factor ( H.C.F.) of two natural numbers is the largest common factor (or divisor) of the given natural numbers. In other words, H.C.F. is the greatest element of the set of common factors of the given numbers.

H.C.F. is also called Greatest Common Divisor ( G.C.D.)

Here, we will discuss about the method of HCF i.e. Highest common factor.

EXAMPLE: Find the HCF of 18 & 21

Factor of 18 are – 1, 2, 3, 6, 9, 18 i.e, –

1×18=18

2×9=18

3×6=18

Factor of 21 are – 1, 3, 7, 21 i.e, –

1×21=21

7×3=21

We noticed that the Highest common factor of 18 and 21 is 3.

3 is the HCF of 18 & 21.

### Method To Find HCF Of Numbers

There are basically three methods of finding HCF of two or more numbers.

1- Factorization method

2- Prime Factorization method

3- Division method

### Factorization method

Example:: Find the HCF of 26 and 35

Solution:
Now find all factors of 26

Factors of 26 are – 1, 2, 13, 26

Now find all the factors of 35

Factors of 35 are – 1, 5, 7, 35

HCF of 26 & 35 is 1.

### Prime factorization method

Example: Find the HCF of 36,45,48

Solution:
Now find the prime factor for each number.

36 = 2 × 2 × 3 × 3

45 = 3 × 3 × 5

48 = 2 × 2 × 2 × 2 x3

The common prime factor = 3

HCF = 3

### Division method

Example: Find the HCF of 16 and 21

Solution:
Step 1- Here, take smallest number i.e, 16 as divisor and bigger number i.e, 21 as dividend.

Step 2- Now, the remainder 5 becomes the divisor and the divisor 16 becomes the dividend.

Step 3- Now, repeat these steps until the remainder becomes zero. And the last divisor will your HCF.