MyMaths MyLife

Facts And Formulae:

Highest Common Factor:(H.C.F) or Greatest Common Meaure(G.C.M) :
The H.C.F of two or more than two numbers is the greatest
number that divides each of them exactly.

There are two methods :

i.Factorization method: Express each one of the given numbers as
the product of prime factors. The product of least powers of common
prime factors gives HCF.

Example : Find HCF of 26 * 32*5*74 , 22 *35*52 * 76 ,
2*52 *72
Solution: The prime numbers given common numbers are 2,5,7
Therefore HCF is 22 * 5 *72 .

ii.Division Method : Divide the larger number by smaller one. Now
divide the divisor by remainder. Repeat the process of dividing
preceding number last obtained till zero is obtained as number. The
last divisor is HCF.


Least common multiple[LCM] : The least number which is
divisible by each one of given numbers is LCM.

There are two methods for this:

i.Factorization method : Resolve each one into product of prime
factors. Then LCM is product of highest powers of all factors.

ii.Common division method.

The basic number system we use in maths are:

Natural Numbers:
The numbers we use for counting are called natural numbers. The set of all natural numbers is denoted by “N”.
Hence N= {1,2,3,4……..}.

Whole Numbers:
When all the natural numbers and zero are put together, we get a new set of whole numbers. The set of whole numbers is denoted by “W”.
Hence W={0,1,2,3,4………}.

Integers:
The set containing positive numbers(1,2,3….), negative numbers(-1,-2,-3,…..) together with zero is called as set of integers. We denote the set of integers with “Z”.
Hence Z={……-3,-2,-1,0,1,2,3,……..}.

Rational Numbers:
A rational number is a number of the form a/b. Where a and b are integers, b≠0.
Example: {2/3, 4/7,7/9……..}

Prime Numbers:
Numbers which do not have any other factors except 1 and itself are called prime numbers.
Examples: {1,2,3,5,7,11,13,17,19,23,29,31,37,41……….}

Composite Numbers:
All numbers greater than 1 and except prime numbers are called composite numbers.
Examples: {4,6,8,9,10,12…….}.

Even Numbers:
Numbers which are exactly divisible by 2 are called even numbers.
Examples: {2,4,6,8,10…….}

Odd Numbers:
Numbers which are not exactly divisible by 2 are called even numbers.
(or)
Numbers which are not even numbers are called odd numbers.
Examples: {1,3,5,7,9……..}.