GCF of 200/205, 2430/140
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 200/205, 2430/140 i.e 10/5740 easily. The following is the detailed procedure to determine the greatest common factor of fractions 200/205, 2430/140.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
What is the GCF of 200/205,2430/140?
Given fractions are 200/205,2430/140
To find the GCF of fractions, we have to find the GCF of numerator numbers and LCM of denominator numbers. Its formula is given by
GCF of Fraction = Greatest Common Factor of Numerator/Least Common Multiple of Denominators
In the fractions 200/205,2430/140, numerators are 200,2430
Denominators are 205,140
The GCF of 200,2430 is 10 .
LCM of 205,140 is 5740.
The greatest common factor of 200/205,2430/140 = [GCF of 200,2430]/[LCM of 205,140]= 10/5740
Therefore, the GCF of 200/205,2430/140 is 10/5740.
To find the highest common factor of 200,2430, we have to find the factors of both numbers and list the highest common factor.
The factors of 200 are 1, 2, 4, 5, 8, 10, 20, 25, 40, 50, 100, 200
The factors of 2430 are 1, 2, 3, 5, 6, 9, 10, 15, 18, 27, 30, 45, 54, 81, 90, 135, 162, 243, 270, 405, 486, 810, 1215, 2430
The HCF of 200,2430 is 10.
Lets's calculate GCF of 200,2430
| 2 | 200, 2430 |
| 5 | 100, 1215 |
| 20, 243 |
∴ So the GCF of the given numbers is 2 x 5 = 10
Greatest Common Factor of 200,2430 By Matching Biggest Common Factor Method
Now, list down the factors of 200
:1,2,4,5,8,10,20,25,40,50,100,200
Now, list down the factors of 2430
:1,2,3,5,6,9,10,15,18,27,30,45,54,81,90,135,162,243,270,405,486,810,1215,2430
Greatest Common Factor
We found the factors 200,2430 . The biggest common factor number is the GCF number.
So the greatest common factor 200,2430 is 10.
Lets's calculate LCM of 205,140
| 5 | 205, 140 |
| 41, 28 |
∴ So the LCM of the given numbers is 5 x 41 x 28 = 5740
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 10/5740
Therefore, the GCF of Fractions 200/205,2430/140 is 10/5740
Least Common Multiple of 205,140 with GCF Formula
The formula of LCM is LCM(a1,a2,a3....,an) = ( a1 × a2 × a3 × .... × an) / GCF(a1,a2,a3....,an) x common factors(if more than 2 numbers have common factors).
We need to calculate greatest common factor of 205,140 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(205,140) = 5
common factors(in case of two or more numbers have common factors) = 1
GCF(205,140) x common factors =5 x 1 = 5
LCM(205,140) = ( 205 × 140 ) / 5
LCM(205,140) = 28700 / 5
LCM(205,140) = 5740
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FAQs on GCF of Fractions of 200/205, 2430/140
1. What is the HCF of 200,2430?
The HCF of 200,2430 is 10
2. What is the GCF of a fraction?
The GCF of a fraction is defined as the greatest fraction that divides exactly into 2 or more fractions.
3. How to find GCF in Fractions?
Answer: GCF of fractions can be found using the simple formula GCF of Fractions = GCF of Numerators/LCM of Denominators.
4. What is the GCF of Fractions for 200/205, 2430/140?
Answer: GCF of Numerators as per given numbers 200/205, 2430/140 is
GCF of Numerators i.e. for 200,2430 is 10
LCM of denominators i.e. for 205,140 is 5740.
Thus, GCF of Fractions is 10/5740.Finally, GCF of Fractions for 200/205, 2430/140 is 10/5740.