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What is the greatest common divisor and how to find the greatest common divisor of two numbers.

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Greatest common divisor:                                                The greatest common divisor of  two integers a and b.Which are not both zero is the largest integer that divides both a and b.Which is written as (a,b) and is also written as,     gcd(a,b) The  greatest common divisor is a number which should divide the number a and b,Now we find the gcd of some numbers as under. For example:  Find the gcd of  24 and 30. First find the divisors of  24 and 30  we have.         24 = 1,2,3,4,6,8,12,24         30 = 1,2,3,5,6,10,15,30 Now we seen that there are many common divisors of 24 and 30.these are (1,2,3,6) but we have to chose the largest number which is a common divisor of 24 and 30.Here 6 is the largest integer that is the greatest common divisor of both 24 and 30.So 6 is the greatest common divisor of 24 and 30. Another example:      find the gcd of    20 and 35.            Factors of 20 and 35. 20=1,2,4,5,10,20 35=1,5,7,35 So the greatest com
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What is Greatest integer function and frictional part.

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Greatest integer function:                                                   The greatest integer function is a real number  x, denoted by [x] is the largest integer less than or equal to x. The equation of the greatest integer function is:                                         [x] ≦ x < [x] + 1 For example: x= 5.6 Then the greater integer function of x is. [x]=[5.6]=5 Lets do a proof. Show that if n is an integer than [x+n]=n+[x],where x is a real number. solution: proof      Let [x]=m, so m is an integer  this implies that,      m ≦  x < m + 1 now adding n to the inequality we get.     m + n ≦ x +n < m + n +1 This shows that m + n is the largest integer less than or equal to x + n,    [x + n]=m + n               as , m=[x] so,  [x + n]= [x] + n Fractional part:             The fractional part of a real number x,denoted by {x}, is the difference  of  x - [x], Where [x] is the greater integer function. For example: the fri
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What is probability?

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Definition of probability:                                                 Probability is the the chance of occurrence of an event in the present or in future.When we  talk about the probability of  an event we basically mean the chance of the even. For example:                      when we want to know about the weather of our city.We are saying that  will it be sunny day or rainy day tomorrow.We are talking about the chance of rainy and sunny day.The chance of rainy or sunny is  50 50 .It may be possible that tomorrow will be a rainy day but it may be sunny.we can not say that it will be sunny.Because we do not know the exact condition. Another example:                            In the tossing of a cricket match.The probability of appearing of head or tail is 50 50. Both the team captains have a equal chance to win the toss. 
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How to multiply,add and subtract two matrices.

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Matrices Multiplication.                                             Matrix multiplication is done in a very easy manner.In matrix multiplication we multiply the rows of the first matrix with the column of the second matrix.It is very important that the number of columns in the first matrix should be equal to the number of rows in the second matrix. Matrix addition:                        In matrix addition we add the first element of the first matrix with the first element of the second matrix,the second element of first with the second of the second and in the same manner we add the same position elements each other. Matrix subtraction:                                 Subtraction is also done in the same way as the addition is done.
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How to find mode and range of a data.

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Mode;           Mode is define as the most repeated value in the data set.We will take a sample of data and than find its mode. For example:                      1,3,4,5,6,7,8,6,4,5,2,3,4,6,5,4,5,6,5,7,5,8,6,7,5 So in this data 5 is repeated more than other values.So the mode for this data is 5. Range:              Range is define as the difference between the lowest value of the data and the highest value. For example we have the following data set.                                 {3,6,8,4,2.9} So,     Range=highest value - lowest value Here we have the highest value of the data is 9 and the smallest value is 2. Range=9-2           =7 hence the range for the above data is 7                    
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HOW TO FIND MEAN AND MEDIAN OF A DATA.

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Mean: Mean is usually known as average of data.Which is equal to the sum of total numbers divided by the total numbers. Now we interpret it mathematically by a formula. Mean=sum of total numbers ∕total numbers Now we have data as below.We want to find its mean.                          3,5,6,7,4,8,9,3,9 than the mean is,                            mean=3+5+6+7+4+8+9+3+9 / 9                        mean= 54/9                                  =6 so mean is 6 for the above data Median;              Median is the central value of the data.It mean the middle value of the date.There are two formulas to find the mean.First one is when the data is odd. and the second is when the data is even. Even and odd is decided on the basis of n.n is the total numbers. For odd data the formula is,                     Median=[(n+1)/2]th value.  Here n is total numbers. For even data we add the two middle values and divide it with 2. Let's take the following d
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HOW TO FIND LCM and HCF OF NUMBERS.

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First we will find LCM of any two numbers. First of all what is LCM.LCM mean the least(smallest) common multiple.It mean the common number which divides the given numbers and is the smallest number greater than 1. For example: Find the LCM of  8 and 12  First find the factors of 8. 1✕8=8 2✕4=8 4✕2=8 8✕1=8 So the factors of 8 are 1,2,4,8 Now find the factors of 12. 1✕12=12 2✕6=12 3✕4=12 4✕3=12 6✕2=12 12✕1=12 So the factors of 112 are 1,2,3,4,6,12 Now factors of 8 and 12 are  Factors of 8.   1,2,4,8 Factors of 12. 1,2,3,4,6,12 So the least common multiple of 8 and 12 is 2. Now we will find the H.C.F. H.C.F stands for highest common factor.It means a number which is factor of the given numbers and is the largest number. Now let we take number 8 and 12 again.Now we will find their H.C.F. The factor of 8 and 12 are as follow Factors of 8.   1,2,4,8 Factors of 12. 1,2,3,4,6,12 The highest common factor of 8 and 12 is 4. In th
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