HCF and GCD

Here i have a new topic which will help you solve the factors, HCF is the Highest Common factor. But before that i will just give you an introduction of Factors which will help you understand this more better.

In algebraic equation each term is the product of one or more numbers. These numbers are known as factors of that term. Isn't it simple. Well, now let me explain you about HCF.

HCF is also called as Greatest common divisior(GCD). HCF of two or more numbers is the greatest number that can be divided by each one of the numbers.

This term HCF can be calculated with different methods such as

1. Factorization Method: The numbers are expressed as product of prime factors. The product of least powers of common prime factors gives HCF.

Here is an example for this method. Lets find the HCF for 36, 90, 72
36 = 2² × 3²
90 = 2 × 5 × 3²
72 = 2³ × 3²
The least power of 2 in the set is - 2
The least power of 3 in the set is - 3²
3² × 2 = 9 × 2 = 18, here 18 is the GCB or the HCF.

2. Division Method: To find the HCF of the two given numbers, divide the large number by the small numbers same way divide the divident by the reminder. This procedure has to repeated until you get zero(0). The last dividend is the HCF of the two numbers.

Here lets find the HCF for 27 and 36
First divide 36/27 the reminder would be 9
now the next step is divide the dividend to the reminder i.e. 27/9 and the answer you get is 0.
Therefore the HCF of 27 and 36 is 9.

Isn't this easy....I have solved two problems using Two easy methods to find the HCF, try this out using your own numbers and leave your comment.