Greatest Common Factors

GREATEST COMMON FACTOR ( G.C.F):

It is also called as Highest Common Factor( H.C.F) or Greatest Common Divisor( G. C.D).

Greatest Common Factor is the greatest factor of the numbers that divides the given numbers exactly.

If any common factor is not obtained for the numbers, then the G.C.F of the numbers is 1.

The G.C.F of numbers can be find out by any one of the methods. They are:

1) G.C.F by Listing out the Factors.

2)  G.C.F by using Factor-tree method.

3) G.C.F by using Short Division method.

The G.C.F obtained by any one of the above methods is Same.

 

1) G.C.F by Listing Out the Factors:

(i) We need to find the factors of the given numbers.

(ii)  The Common factors of the numbers are taken out.

(iii)  The greatest factor in those Common factors is the G.C.F.

 

 

Let the numbers be: 18 and 24.

Answer:

i) Factors of 18: 1, 2, 3, 6, 9, 18.

ii) Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24.

Therefore, Common Factors of 18 and 24 : 1, 2, 3, 6.

Thus, the Greatest Common Factor(G.C.F) or H.C.F or G.C.D = 6.

 

2) G.C.F by Prime Factorization:

i) In this method, we need to find out the Prime factors of the given numbers either by Factor-tree method or Short division method.

ii) The common factors of the numbers are taken out.

iii) Those common factors obtained are multiplied, which gives the Greatest Common Factor.   

Let the numbers be : 18 and 24.

Answer:

Factors of 18:   Prime Factors of 18      = 2 * 3* 3	Factors of 60: Prime Factors of 60        = 2*2*3*5
Common factors of 18 and 60 = 2, 3. Greatest Common factor = 2*3 = 6.

                                                     

 

3) G.C.F by Short Division method:

i) The Prime factors of the numbers are found out by using Short division method.

ii) The common factors of the numbers are taken out.

iii) We need to multiply these common factors of the numbers, which gives Greatest Common Factors (G.C.F) of the given numbers.

 

Let the numbers be : 18 and 24.

Answer:

Factor of 18                                           Prime Factor of 18           =  2*3*3	Factor of 24                                                                                         Prime Factor of 24            = 2*2*2*3
Common Factors of 18 and 24 = 2, 3. Greatest Common Factor (G.C.F) of 18 and 24   = 2*3 = 6.

 

Find the Highest Common Factor:

1) 24 , 36 and 60.

Answer:

Finding H.C.F  by using  Factor-tree method:

 

 

Factors of 24 Factors of 24  = 2*2*2*3	Factors of 36 Factors of 36 = 2*2*3*3	Factors of 60 Factors of 60 = 2*2*3*5
Common Factors of 24, 36, and 60 = 2 , 2, 3. Highest Common Factor = 2 * 2* 3 = 12.

 

2) 18 and 25.

Answer:

Finding G.C.F by Listing out Factors method.

i) Factors of 18 =  1 , 2, 3, 6, 9, 18.

ii) Factors of 25 =  1, 5 ,25.

Therefore, Common factors of 18 and 25 = 1.

Here, Common factors are not their except factor 1.

Thus, the G.C.F of 18 and 25 = 1.

 

3) 16 and 30

Answer:

i) Factors of 16 = 1, 2, 4 , 8 ,16.

ii) Factors of 30 = 1, 2, 3, 5, 6, 10, 15, 30.

Therefore, Common factors of 16 and 30 =  1, 2.

Thus,Greatest Common Divisor ( G.C.D) =  2.

 

4) 36 , 54 and 63.

Answer:

i) Factors of 36 =  1, 2, 3, 4, 6, 9, 12, 18, 36.

ii) Factors of 54 = 1, 2, 3, 6, 9, 18, 27, 54.

iii) Factors of 63 = 1, 3, 7, 9, 21 ,63.

Therefore, Common Factors of 36, 54 and 63 =  1, 3, 9.

Thus, Greatest Common Factor (G.C.F) = 9.