H.C.F. (Highest Common Factor)

We are using 3 names for Highest Common Factor

H.C.F. = Highest Common Factor

G.C.D. = Greatest Common Divisor

G.C.M. = Greatest Common Measure

We take an example of Division :  17/3 (17 Divide by 3)

Result:

Remainder = 2,

Quotient = 5,

Divisor = 3,

Dividend = 17.

Factor: If any Number is divided by another number then we can say that, That number is factor of this number.

Examples of Factor : 

12 = 1, 2, 3, 4, 6, 12.

15 = 1, 3, 5, 15.

24 = 1, 2, 3, 4, 6, 8, 12, 24.

56 = 1, 2, 4, 7, 8, 14, 28, 56.

Prime Factor: If any Number is divided by any prime number then we can say that, That Prime number is factor of this number.

Examples of Prime Factor : We are taking number only one time as per given below examples

12 = 2*2*3     = 2, 3 

15 = 3*5         = 3, 5 

24 = 2*2*2*3 = 2, 3

56 = 2*2*2*7 = 2, 7

There are 2 methods in H.C.F.

1) Factorization Method

2) Division Method

1) Factorization Method:

If we want to find the HCF of 2 or more than 2 numbers at that time we calculate prime factor of each number and take common factors from all number and multiply those number.

Example : Find the HFC/GCD of 12 & 15

Solution  :  12 = 2*2*3*

                    15 = 3*5

                   So, HCF/GCD = 3  Which is common in both.

 

2) Division Method:

If we want to find the HCF of 2 or more than 2 numbers at that time we have to divide Highest number by Lowest number, then Remainder is being divisor and divisor is being Dividend, This cycle is repeat till we get  Remainder = 0.When we get reminder 0 at that time Divisor = HCF

Example : Find the HFC/GCD of 12 & 15

Solution  :  

                                1       

                      12 )  15

                              12      4   

                              03  ) 12                     

                                      12     

                                      00

       

                                         H.C.F. = 3

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Questions:

1) Find HCF/GCD of 18, 24 & 36 with the help of Factorization Method.

    Ans: 6

              Prime Factor of 18 = 2 *3*3

                                        24 = 2*2*2*3

                                        36 = 2*2*3*3

              HCF/GCD = 2*3 = 6

2) Find the Greatest Number that exactly divides 36, 84, 132, 180 with the help of Factorization                  Method.       

    Ans: 12

              Prime Factor of 36   = 2*2*3*3

                                        84   = 2*2*3*7

                                        132 = 2*2*3*11

                                        180   = 2*2*3*3*5

              HCF/GCD = 2*2*3 = 12

3) Find the H.C.F. of 18, 36 & 84 with the help of Division Method.

    Ans: 6

                        2                                                    

               36 ) 84                                                

                      72       3                                             

                      12 )  36                                                

                              36                                                      

                              00                                                      

                        1    

               12) 18

                     12      2       

                       6 ) 12

                            12        

                            00

              HCF/GCD = 6