GCF of 7140/749, 8092/1988
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 7140/749, 8092/1988 i.e 476/212716 easily. The following is the detailed procedure to determine the greatest common factor of fractions 7140/749, 8092/1988.
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 7140/749,8092/1988?
Given fractions are 7140/749,8092/1988
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 7140/749,8092/1988, numerators are 7140,8092
Denominators are 749,1988
The GCF of 7140,8092 is 476 .
LCM of 749,1988 is 212716.
The greatest common factor of 7140/749,8092/1988 = [GCF of 7140,8092]/[LCM of 749,1988]= 476/212716
Therefore, the GCF of 7140/749,8092/1988 is 476/212716.
To find the highest common factor of 7140,8092, we have to find the factors of both numbers and list the highest common factor.
The factors of 7140 are 1, 2, 3, 4, 5, 6, 7, 10, 12, 14, 15, 17, 20, 21, 28, 30, 34, 35, 42, 51, 60, 68, 70, 84, 85, 102, 105, 119, 140, 170, 204, 210, 238, 255, 340, 357, 420, 476, 510, 595, 714, 1020, 1190, 1428, 1785, 2380, 3570, 7140
The factors of 8092 are 1, 2, 4, 7, 14, 17, 28, 34, 68, 119, 238, 289, 476, 578, 1156, 2023, 4046, 8092
The HCF of 7140,8092 is 476.
Lets's calculate GCF of 7140,8092
| 2 | 7140, 8092 |
| 2 | 3570, 4046 |
| 7 | 1785, 2023 |
| 17 | 255, 289 |
| 15, 17 |
∴ So the GCF of the given numbers is 2 x 2 x 7 x 17 = 476
Greatest Common Factor of 7140,8092 By Matching Biggest Common Factor Method
Now, list down the factors of 7140
:1,2,3,4,5,6,7,10,12,14,15,17,20,21,28,30,34,35,42,51,60,68,70,84,85,102,105,119,140,170,204,210,238,255,340,357,420,476,510,595,714,1020,1190,1428,1785,2380,3570,7140
Now, list down the factors of 8092
:1,2,4,7,14,17,28,34,68,119,238,289,476,578,1156,2023,4046,8092
Greatest Common Factor
We found the factors 7140,8092 . The biggest common factor number is the GCF number.
So the greatest common factor 7140,8092 is 476.
Lets's calculate LCM of 749,1988
| 7 | 749, 1988 |
| 107, 284 |
∴ So the LCM of the given numbers is 7 x 107 x 284 = 212716
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 476/212716
Therefore, the GCF of Fractions 7140/749,8092/1988 is 476/212716
Least Common Multiple of 749,1988 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 749,1988 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(749,1988) = 7
common factors(in case of two or more numbers have common factors) = 1
GCF(749,1988) x common factors =7 x 1 = 7
LCM(749,1988) = ( 749 × 1988 ) / 7
LCM(749,1988) = 1489012 / 7
LCM(749,1988) = 212716
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FAQs on GCF of Fractions of 7140/749, 8092/1988
1. What is the HCF of 7140,8092?
The HCF of 7140,8092 is 476
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 7140/749, 8092/1988?
Answer: GCF of Numerators as per given numbers 7140/749, 8092/1988 is
GCF of Numerators i.e. for 7140,8092 is 476
LCM of denominators i.e. for 749,1988 is 212716.
Thus, GCF of Fractions is 476/212716.Finally, GCF of Fractions for 7140/749, 8092/1988 is 476/212716.