GCF of 7340/209, 6180/5497
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 7340/209, 6180/5497 i.e 20/1148873 easily. The following is the detailed procedure to determine the greatest common factor of fractions 7340/209, 6180/5497.
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 7340/209,6180/5497?
Given fractions are 7340/209,6180/5497
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 7340/209,6180/5497, numerators are 7340,6180
Denominators are 209,5497
The GCF of 7340,6180 is 20 .
LCM of 209,5497 is 1148873.
The greatest common factor of 7340/209,6180/5497 = [GCF of 7340,6180]/[LCM of 209,5497]= 20/1148873
Therefore, the GCF of 7340/209,6180/5497 is 20/1148873.
To find the highest common factor of 7340,6180, we have to find the factors of both numbers and list the highest common factor.
The factors of 7340 are 1, 2, 4, 5, 10, 20, 367, 734, 1468, 1835, 3670, 7340
The factors of 6180 are 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60, 103, 206, 309, 412, 515, 618, 1030, 1236, 1545, 2060, 3090, 6180
The HCF of 7340,6180 is 20.
Lets's calculate GCF of 7340,6180
| 2 | 7340, 6180 |
| 2 | 3670, 3090 |
| 5 | 1835, 1545 |
| 367, 309 |
∴ So the GCF of the given numbers is 2 x 2 x 5 = 20
Greatest Common Factor of 7340,6180 By Matching Biggest Common Factor Method
Now, list down the factors of 7340
:1,2,4,5,10,20,367,734,1468,1835,3670,7340
Now, list down the factors of 6180
:1,2,3,4,5,6,10,12,15,20,30,60,103,206,309,412,515,618,1030,1236,1545,2060,3090,6180
Greatest Common Factor
We found the factors 7340,6180 . The biggest common factor number is the GCF number.
So the greatest common factor 7340,6180 is 20.
Lets's calculate LCM of 209,5497
Given numbers has no common factors except 1. So, there LCM is their product i.e 1148873
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 20/1148873
Therefore, the GCF of Fractions 7340/209,6180/5497 is 20/1148873
Least Common Multiple of 209,5497 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 209,5497 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(209,5497) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(209,5497) x common factors =1 x 1 = 1
LCM(209,5497) = ( 209 × 5497 ) / 1
LCM(209,5497) = 1148873 / 1
LCM(209,5497) = 1148873
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FAQs on GCF of Fractions of 7340/209, 6180/5497
1. What is the HCF of 7340,6180?
The HCF of 7340,6180 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 7340/209, 6180/5497?
Answer: GCF of Numerators as per given numbers 7340/209, 6180/5497 is
GCF of Numerators i.e. for 7340,6180 is 20
LCM of denominators i.e. for 209,5497 is 1148873.
Thus, GCF of Fractions is 20/1148873.Finally, GCF of Fractions for 7340/209, 6180/5497 is 20/1148873.