GCF of 7860/584, 8188/9730
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 7860/584, 8188/9730 i.e 4/2841160 easily. The following is the detailed procedure to determine the greatest common factor of fractions 7860/584, 8188/9730.
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 7860/584,8188/9730?
Given fractions are 7860/584,8188/9730
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 7860/584,8188/9730, numerators are 7860,8188
Denominators are 584,9730
The GCF of 7860,8188 is 4 .
LCM of 584,9730 is 2841160.
The greatest common factor of 7860/584,8188/9730 = [GCF of 7860,8188]/[LCM of 584,9730]= 4/2841160
Therefore, the GCF of 7860/584,8188/9730 is 4/2841160.
To find the highest common factor of 7860,8188, we have to find the factors of both numbers and list the highest common factor.
The factors of 7860 are 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60, 131, 262, 393, 524, 655, 786, 1310, 1572, 1965, 2620, 3930, 7860
The factors of 8188 are 1, 2, 4, 23, 46, 89, 92, 178, 356, 2047, 4094, 8188
The HCF of 7860,8188 is 4.
Lets's calculate GCF of 7860,8188
| 2 | 7860, 8188 |
| 2 | 3930, 4094 |
| 1965, 2047 |
∴ So the GCF of the given numbers is 2 x 2 = 4
Greatest Common Factor of 7860,8188 By Matching Biggest Common Factor Method
Now, list down the factors of 7860
:1,2,3,4,5,6,10,12,15,20,30,60,131,262,393,524,655,786,1310,1572,1965,2620,3930,7860
Now, list down the factors of 8188
:1,2,4,23,46,89,92,178,356,2047,4094,8188
Greatest Common Factor
We found the factors 7860,8188 . The biggest common factor number is the GCF number.
So the greatest common factor 7860,8188 is 4.
Lets's calculate LCM of 584,9730
| 2 | 584, 9730 |
| 292, 4865 |
∴ So the LCM of the given numbers is 2 x 292 x 4865 = 2841160
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 4/2841160
Therefore, the GCF of Fractions 7860/584,8188/9730 is 4/2841160
Least Common Multiple of 584,9730 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 584,9730 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(584,9730) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(584,9730) x common factors =2 x 1 = 2
LCM(584,9730) = ( 584 × 9730 ) / 2
LCM(584,9730) = 5682320 / 2
LCM(584,9730) = 2841160
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FAQs on GCF of Fractions of 7860/584, 8188/9730
1. What is the HCF of 7860,8188?
The HCF of 7860,8188 is 4
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 7860/584, 8188/9730?
Answer: GCF of Numerators as per given numbers 7860/584, 8188/9730 is
GCF of Numerators i.e. for 7860,8188 is 4
LCM of denominators i.e. for 584,9730 is 2841160.
Thus, GCF of Fractions is 4/2841160.Finally, GCF of Fractions for 7860/584, 8188/9730 is 4/2841160.