Highest Common Factor (H.C.F.)

H.C.F that is highest common factor is also called G.C.D i.e. Greatest Common Divisor is the greatest or highest number which exactly divides two or more numbers.


Steps to find out the H.C.F (Highest Common factor)

Step I: First find out the prime factors of each of the numbers

Step II: Then find out the common prime factor of those numbers

Step III: The product of lower power of common factors is the H. C. F

Here are few examples to illustrate H. C. F (Highest Common Factor)

1. Find the H.C.F of 27 and 36

Solution:

The factors of 27 = 3 × 3 × 3 = 33

The factors of 36 = 2 × 2 × 3 × 3 = 2× 32

The common prime factor is 3

The lowest power of 3 is 32

Therefore, H. C. F = 3 × 3 = 9


2. Find the H.C.F of 24 and 12

Solution:

The factors of 24 = 2 × 2 × 2 × 3 = 23 × 3

The factors of 12 = 2 × 2 × 3 = 22 × 3

The common prime factors are 2 and 3

The lowest power of 2 is 22

The lowest power of 3 is 3

Therefore, H. C. F = 2 × 2 × 3 = 12


3. Find the H.C.F of 25 and 50

Solution:

The factors of 25 = 5 × 5 = 52 

The factors of 50 = 2 × 5 × 5 = 5× 2

The common prime factor is 5

The lowest power of 5 is 52

Therefore, H. C. F = 5 × 5 = 25


4. Find the H.C.F of 18 and 36

Solution:

The factors of 18 = 2 × 3 × 3 = 2 × 32 

The factors of 36 = 2 × 2 × 3 × 3 = 2× 32

The common prime factors are 2 and 3

The lowest power of 3 is 32

The lowest power of 2 is 2

Therefore, H. C. F = 2 × 3 × 3 = 18


5. Find the H.C.F of 55 and 35

Solution:

The factors of 55 = 5 × 11

The factors of 36 = 5 × 7

The common prime factors is 5

The lowest power of 5 is 5

Therefore, H. C. F = 5


6.Find the H.C.F of 12, 18 and 15

Solution:

The factors of 12 = 2 × 2 × 3 = 22 × 3

The factors of 18 = 2 × 3 × 3 = 2 × 32 

The factors of 15 = 3 × 5 

The common prime factor is 3

The lowest power of 3 is 3

Therefore, H. C. F =  3 


7. Find the H.C.F of 48 and 60

Solution:

The factors of 48 = 2 × 2 × 2 × 2 × 3 = 24 × 3

The factors of 60 = 5 × 2 × 2 × 3 = 5 × 22  ×3

The common prime factors are 2 and 3

The lowest power of 2 is 22

The lowest power of 3 is 3

Therefore, H. C. F = 2 × 2 × 3 = 12

You might like these



5th Grade Math

From Highest Common Factor (H.C.F.) to HOME PAGE

New! Comments

Have your say about what you just read! Leave me a comment in the box below.


Recent Articles

  1. Amphibolic Pathway | Definition | Examples | Pentose Phosphate Pathway

    Jun 06, 24 10:40 AM

    Amphibolic Pathway
    Definition of amphibolic pathway- Amphibolic pathway is a biochemical pathway where anabolism and catabolism are both combined together. Examples of amphibolic pathway- there are different biochemical…

    Read More

  2. Respiratory Balance Sheet | TCA Cycle | ATP Consumption Process

    Feb 18, 24 01:56 PM

    ATP Synthase in Mitochondria
    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…

    Read More

  3. Electron Transport System and Oxidative Phosphorylation | ETC |Diagram

    Feb 04, 24 01:57 PM

    Electron Transport Chains
    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…

    Read More

  4. Tricarboxylic Acid Cycle | Krebs Cycle | Steps | End Products |Diagram

    Jan 28, 24 12:39 PM

    Aerobic Respiration
    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…

    Read More

  5. Aerobic Respiration | Definition of Aerobic Respiration | Glycolysis

    Dec 15, 23 08:42 AM

    Aerobic Respiration
    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…

    Read More