Factors

When a number divides another number exactly the divisor is called a factor of the dividend.

Ex- :

  1.  4 divides  12 exactly, so 4 is a factor of  12.
  2.  7 divides  35 exactly, so  7 is a factor of  35.

Properties

  1. Every non-zero number has a limited number of factors.
  2.  1 is the factor of every number.
  3. Every non-zero number is the largest factor of itself.
  4. Every non-zero number is either less than or equal to the given number.

Highest common factor (HCF)

the \text{HCF} of some given numbers is the largest number that divides each one of them exactly.

Ex- :

Find the \text{HCF} of  6 and 9 .

We have :

6=1,\ 2,\ 3,\ 6 .
 9=1,\ 3,\ 9.
Common factors =1,\ 3.
\text{HCF}=3.

Prime factorisation

The method of expressing a composite number as the product of prime factors is called prime factorisation.

Ex- :

  1. Rendered by QuickLaTeX.com


    36=2\times 2\times 3\times 3  .
  2. Rendered by QuickLaTeX.com


    84=2\times 2\times 3\times 7  .
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