GCF of 2020/342, 8900/5667
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 2020/342, 8900/5667 i.e 20/646038 easily. The following is the detailed procedure to determine the greatest common factor of fractions 2020/342, 8900/5667.
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 2020/342,8900/5667?
Given fractions are 2020/342,8900/5667
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 2020/342,8900/5667, numerators are 2020,8900
Denominators are 342,5667
The GCF of 2020,8900 is 20 .
LCM of 342,5667 is 646038.
The greatest common factor of 2020/342,8900/5667 = [GCF of 2020,8900]/[LCM of 342,5667]= 20/646038
Therefore, the GCF of 2020/342,8900/5667 is 20/646038.
To find the highest common factor of 2020,8900, we have to find the factors of both numbers and list the highest common factor.
The factors of 2020 are 1, 2, 4, 5, 10, 20, 101, 202, 404, 505, 1010, 2020
The factors of 8900 are 1, 2, 4, 5, 10, 20, 25, 50, 89, 100, 178, 356, 445, 890, 1780, 2225, 4450, 8900
The HCF of 2020,8900 is 20.
Lets's calculate GCF of 2020,8900
| 2 | 2020, 8900 |
| 2 | 1010, 4450 |
| 5 | 505, 2225 |
| 101, 445 |
∴ So the GCF of the given numbers is 2 x 2 x 5 = 20
Greatest Common Factor of 2020,8900 By Matching Biggest Common Factor Method
Now, list down the factors of 2020
:1,2,4,5,10,20,101,202,404,505,1010,2020
Now, list down the factors of 8900
:1,2,4,5,10,20,25,50,89,100,178,356,445,890,1780,2225,4450,8900
Greatest Common Factor
We found the factors 2020,8900 . The biggest common factor number is the GCF number.
So the greatest common factor 2020,8900 is 20.
Lets's calculate LCM of 342,5667
| 3 | 342, 5667 |
| 114, 1889 |
∴ So the LCM of the given numbers is 3 x 114 x 1889 = 646038
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 20/646038
Therefore, the GCF of Fractions 2020/342,8900/5667 is 20/646038
Least Common Multiple of 342,5667 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 342,5667 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(342,5667) = 3
common factors(in case of two or more numbers have common factors) = 1
GCF(342,5667) x common factors =3 x 1 = 3
LCM(342,5667) = ( 342 × 5667 ) / 3
LCM(342,5667) = 1938114 / 3
LCM(342,5667) = 646038
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FAQs on GCF of Fractions of 2020/342, 8900/5667
1. What is the HCF of 2020,8900?
The HCF of 2020,8900 is 20
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 2020/342, 8900/5667?
Answer: GCF of Numerators as per given numbers 2020/342, 8900/5667 is
GCF of Numerators i.e. for 2020,8900 is 20
LCM of denominators i.e. for 342,5667 is 646038.
Thus, GCF of Fractions is 20/646038.Finally, GCF of Fractions for 2020/342, 8900/5667 is 20/646038.