# Examples of Greatest Common Factor (G.C.F)

G.C. F (Greatest Common Factor) is same as Highest Common Factor (H.C. F) that is the highest or greatest number by which two or more number is completely divisible without leaving any remainder.

This topic on G.C. F (Greatest Common Factor) will provide a wide range of examples which would be helpful to the learners for their better understanding and knowledge.

Here examples on G.C. F (Greatest Common Factor) are illustrated below:

1. Find the greatest common factor of 77 and 84

Solution:

The prime factors of 77 are= 7 × 11

The prime factors of 84 are: 2 × 2 × 3 × 7 = 2× 3 × 7

The common prime factor of 77 and 84 is 7

The lowest power of 7 is 7

Therefore, G. C. F = 7

2. Find the greatest common factor of 92 and 230

Solution:

The prime factors of 92 are: 2 × 2 × 23 = 2× 23

The prime factors of 230 are: 2 × 5 × 23

The common prime factors of 92 and 230 are 2 and 23

The lowest power of 2 is 2

The lowest power of 23 is 23

Therefore, G. C. F = 2 × 23 = 46

3. Find the greatest common factor of 120, 240, and 360

Solution:

The prime factors of 120 are: 2 × 2 × 2 × 3 × 5 = 23 × 3 × 5

The prime factors of 240 are: 2 × 2 × 2 × 2 × 3 × 5 = 24 × 3 × 5

The prime factors of 240 are: 2 × 2 × 2 × 3 × 3 × 5 = 23 × 32 ×5

The common prime factors of 120, 240 and 360 are 2, 3, 5

The lowest power of 2 is 23

The lowest power of 3 is 3

The lowest power of 5 is 5

Therefore, G. C. F = 23 × 3 × 5 = 2 × 2 × 2 × 3 × 5 = 120

4. Find the greatest common factor of 48 and 96

Solution:

The prime factors of 48 are: 2 × 2 × 2 × 2 × 3 = 24 × 3

The prime factors of 96 are: 2 × 2 × 2 × 2 × 2 × 3 = 25 × 3

The common prime factors of 48 and 96 are 2 and 3

The lowest power of 2 is 24

The lowest power of 3 is 3

Therefore, G. C. F = 24 × 3 = 2 × 2 × 2 × 2 × 3 = 48

5. Find the greatest common factor of 255, 170 and 85

Solution:

The prime factors of 255 are: 5 × 3 × 17

The prime factors of 170 are: 2 × 5 × 17

The prime factors of 85 are: 5 × 17

The common prime factors of 255, 170 and 85 are 5 and 17

The lowest power of 5 is 5

The lowest power of 17 is 17

Therefore, G. C. F = 5 × 17 = 85

## You might like these

• ### Worksheet on Divisibility Rules | Questions on Test of Divisibility

This is a worksheet which will provide few problems on the divisibility rule of 2, 3, 4, 5, 6, 7, 8, 9, and 10. 1. Check whether the following numbers are divisible by 2 or 3 or both? (i) 2562 (ii) 5693 (iii) 2201 (iv) 7480 (v) 5296 (vi) 4062 (vii) 4568 (viii) 1425 (ix) 1110

• ### Problems on Divisibility Rules | Rules to Test of Divisibility | Test

Here are few problems on the divisibility rules of 2, 3, 4, 5, 6, 7, 8, 9, and 10 which will help the learners in revising their concepts on the divisibility rules. 1. Check whether 3456 is divisible by 2? Solution: The last digit is an even number (i.e. 6) hence 3456 is

## Recent Articles

1. ### Respiratory Balance Sheet | TCA Cycle | ATP Consumption Process

Feb 18, 24 01:56 PM

The major component that produced during the photosynthesis is Glucose which is further metabolised by the different metabolic pathways like glycolysis, Krebs cycle, TCA cycle and produces energy whic…

2. ### Electron Transport System and Oxidative Phosphorylation | ETC |Diagram

Feb 04, 24 01:57 PM

It is also called ETC. Electron transfer means the process where one electron relocates from one atom to the other atom. Definition of electron transport chain - The biological process where a chains…

3. ### Tricarboxylic Acid Cycle | Krebs Cycle | Steps | End Products |Diagram

Jan 28, 24 12:39 PM

This is a type of process which execute in a cyclical form and final common pathway for oxidation of Carbohydrates fat protein through which acetyl coenzyme a or acetyl CoA is completely oxidised to c…

4. ### Aerobic Respiration | Definition of Aerobic Respiration | Glycolysis

Dec 15, 23 08:42 AM

This is a type of respiration where molecular free oxygen is used as the final acceptor and it is observed in cell. Site of Aerobic Respiration - Aerobic respiration is observed in most of the eukaryo…