Greatest Common Factor (G.C.F)
H. C. F that is highest common factor is also called Greatest Common Factor (G.C.F). There is actually no difference between the two. Greatest Common Factor is actually the greatest factor of two or more numbers.
Here are few examples on Greatest Common Factor
1. Find the greatest common factor of 56 and 63
Solution:
The prime factors of 56 are: 2 × 2 × 2 × 7 = 23×7
The prime factors of 63 are: 3 × 3 × 7 = 32× 7
The common prime factor of 56 and 63 is 7
The lowest power of 7 is 7
Therefore, G .C.F = 7
2. Find the greatest common factor of 42 and 44
Solution:
The prime factors of 42 are: 2 × 3 × 7
The prime factors of 44 are: 2 × 2 × 11 = 22 × 11
The common prime factor of 42 and 44 is 2
The lowest power of 2 is 2
Hence, G. C. F = 2
3. Find the greatest common factor of 88 and 110
Solution:
The prime factors of 88 are: 2 × 2 × 2 × 11 = 23 × 11
The prime factors of 110 are: 2 × 5 × 11
The common prime factors of 8 and 110 are 2 and 11
The lowest power of 2 is 2
The lowest power of 11 is 11
Hence, G. C. F = 2 × 11 = 22
4. Find the greatest common factor of 450 and 500
Solution:
The prime factors of 450 are: 2 × 5 × 5 × 3 × 3 = 2 × 52 × 32
The prime factors of 500 are: 2 × 2 × 5 × 5 × 5 = 22 × 53
The common prime factors of 450 and 500 are 2 and 5
The lowest power of 2 is 2
The lowest power of 5 is 52
Therefore, G. C. F = 2 × 52 =2 ×5 ×5=50
5. Find the greatest common factor of 18 and 20
Solution:
The prime factors of 18 are: 2 × 3 × 3 = 2 × 32
The prime factors of 20 are: 2 × 2 × 5 = 22 × 5
The common prime factor of 18 and 20 is 2
The lowest power of 2 is 2
Therefore, G. C. F = 2
6. Find the greatest common factor of 35, 28 and 70
Solution:
The prime factors of 35 are: 5 ×7
The prime factors of 28 are: 2 × 2 × 7 = 22 ×7
The prime factors of 70 = 2 × 5 × 7
The common prime factor of 35, 28 and 70 is
The lowest power of 7 is 7
Therefore, G. C. F = 7
7. Find the greatest common factor of 56, 28 and 128
Solution:
The prime factors of 56 are: 2 × 2 × 2 × 7 = 23 × 7
The prime factors of 28 are: 2 × 2 × 7 = 22 × 7
The prime factors of 128 are: 2 × 2 × 2 × 2 × 2 × 2 × 2 = 27
The common prime factor of 56, 28 and 128 is 2
The lowest power of 2 is 22
Therefore, G. C. F = 2 × 2 = 4
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 Greatest Common Factor (G.C.F) to HOME PAGE
Recent Articles
-
Definition of Respiratory Quotient | calculation | Application | Plant
Dec 02, 24 12:09 AM
Definition of respiration quotient- the ratio of the carbon-dioxide evolved to that of the oxygen consumed by a cell, tissue, plants or animals in a given time is called respiratory quotient. It is us… -
Amphibolic Pathway | Definition | Examples | Pentose Phosphate Pathway
Jun 06, 24 10:40 AM
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… -
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…
New! Comments
Have your say about what you just read! Leave me a comment in the box below.