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 = 22 × 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 = 52 × 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 = 22 × 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
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
From Highest Common Factor (H.C.F.) to HOME PAGE
Recent Articles
-
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… -
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… -
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… -
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… -
Fermentation | Definition | Types of Fermentation | Application
Nov 29, 23 10:27 PM
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…
New! Comments
Have your say about what you just read! Leave me a comment in the box below.