Examples to find Highest Common Factor by using Prime Factorization Method

This topic would deal with finding the highest common factor using the prime factorization method. With the help of this method we will first find the prime factors of the numbers and then sort out the common factor. Next step is to find the lowest power of those common factors and find out their product. That product would be the highest common factor.

Here are few examples to illustrate on finding the highest common factor using the prime factorization method:

1. Find out the highest common factor of 256 and 224 by prime factorization method:

Solution:

Examples to find Highest Common Factor by using Prime Factorization Method

The prime factors of 256 = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 = 28

The prime factors of 224 = 2 × 2 × 2 × 2 × 2 × 7 = 25 × 7

The common prime factor of 256 and 224 is 2

The lowest power of 2 is 25

Therefore, the H.C.F of 256 and 224 is 25 = 2 × 2 × 2 × 2 × 2 = 32


2. Find out the highest common factor of 24 and 25 by prime factorization method:

Solution:

Examples to find Highest Common Factor by using Prime Factorization Method

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

The prime factors of 25 = 5 × 5 = 52

The common prime factor of 24 and 25 is 1

Therefore, the H.C.F of 24 and 25 is 1


3. Find out the highest common factor of 105 and 124 by prime factorization method:

Solution:

Examples to find Highest Common Factor by using Prime Factorization Method

The prime factors of 105 = 5 × 3 × 7 

The prime factors of 124 = 2 × 2 × 31 = 22 × 31

The common prime factor of 105 and 124 is 1

Therefore, the H.C.F of 105 and 124 is 1


4. Find out the highest common factor of 155 and 55 by prime factorization method:

Solution:

Examples to find Highest Common Factor by using Prime Factorization Method

The prime factors of 155 = 5 × 31 

The prime factors of 55 = 5 × 11 

The common prime factor of 155 and 55 is 5

The lowest power of 5 is 5

Therefore, the H.C.F of 155 and 55 is 5


5. Find out the highest common factor of 48 and 60 by prime factorization method:

Solution:

Examples to find Highest Common Factor by using Prime Factorization Method

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

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

The common prime factors of 48 and 60 are 2 and 3

The lowest power of 2 is 22

The lowest power of 3 is 3

Therefore, the H.C.F of 48 and 60 is 22 × 3 = 2 × 2 × 3 = 12


6. Find out the highest common factor of 12 and 20 by prime factorization method:

Solution:

Examples to find Highest Common Factor by using Prime Factorization Method

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

The prime factors of 20 = 2 × 2 × 5 = 2× 5

The common prime factor of 48 and 60 is 2 

The lowest power of 2 is 22

Therefore, the H.C.F of 12 and 20 is 2 = 2 × 2 = 4

You might like these




5th Grade Math

From Examples to find Highest Common Factor by using Prime Factorization Method to HOME PAGE


New! Comments

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


Recent Articles

  1. 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

  2. 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

  3. 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

  4. 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

  5. Fermentation | Definition | Types of Fermentation | Application

    Nov 29, 23 10:27 PM

    Fermentation
    Definition of fermentation- It is a process that is energy yielding process of anaerobic oxidation of organic compounds which are carried out by the enzyme action of micro organisms where neither gase…

    Read More