GCF of 7198/584, 9231/5230
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 7198/584, 9231/5230 i.e 1/1527160 easily. The following is the detailed procedure to determine the greatest common factor of fractions 7198/584, 9231/5230.
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 7198/584,9231/5230?
Given fractions are 7198/584,9231/5230
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 7198/584,9231/5230, numerators are 7198,9231
Denominators are 584,5230
The GCF of 7198,9231 is 1 .
LCM of 584,5230 is 1527160.
The greatest common factor of 7198/584,9231/5230 = [GCF of 7198,9231]/[LCM of 584,5230]= 1/1527160
Therefore, the GCF of 7198/584,9231/5230 is 1/1527160.
To find the highest common factor of 7198,9231, we have to find the factors of both numbers and list the highest common factor.
The factors of 7198 are 1, 2, 59, 61, 118, 122, 3599, 7198
The factors of 9231 are 1, 3, 17, 51, 181, 543, 3077, 9231
The HCF of 7198,9231 is 1.
Lets's calculate GCF of 7198,9231
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 7198,9231 By Matching Biggest Common Factor Method
Now, list down the factors of 7198
:1,2,59,61,118,122,3599,7198
Now, list down the factors of 9231
:1,3,17,51,181,543,3077,9231
Greatest Common Factor
We found the factors 7198,9231 . The biggest common factor number is the GCF number.
So the greatest common factor 7198,9231 is 1.
Lets's calculate LCM of 584,5230
| 2 | 584, 5230 |
| 292, 2615 |
∴ So the LCM of the given numbers is 2 x 292 x 2615 = 1527160
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/1527160
Therefore, the GCF of Fractions 7198/584,9231/5230 is 1/1527160
Least Common Multiple of 584,5230 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 584,5230 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(584,5230) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(584,5230) x common factors =2 x 1 = 2
LCM(584,5230) = ( 584 × 5230 ) / 2
LCM(584,5230) = 3054320 / 2
LCM(584,5230) = 1527160
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FAQs on GCF of Fractions of 7198/584, 9231/5230
1. What is the HCF of 7198,9231?
The HCF of 7198,9231 is 1
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 7198/584, 9231/5230?
Answer: GCF of Numerators as per given numbers 7198/584, 9231/5230 is
GCF of Numerators i.e. for 7198,9231 is 1
LCM of denominators i.e. for 584,5230 is 1527160.
Thus, GCF of Fractions is 1/1527160.Finally, GCF of Fractions for 7198/584, 9231/5230 is 1/1527160.