GCF of 7140/530, 3878/7266
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 7140/530, 3878/7266 i.e 14/1925490 easily. The following is the detailed procedure to determine the greatest common factor of fractions 7140/530, 3878/7266.
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 7140/530,3878/7266?
Given fractions are 7140/530,3878/7266
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 7140/530,3878/7266, numerators are 7140,3878
Denominators are 530,7266
The GCF of 7140,3878 is 14 .
LCM of 530,7266 is 1925490.
The greatest common factor of 7140/530,3878/7266 = [GCF of 7140,3878]/[LCM of 530,7266]= 14/1925490
Therefore, the GCF of 7140/530,3878/7266 is 14/1925490.
To find the highest common factor of 7140,3878, 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 3878 are 1, 2, 7, 14, 277, 554, 1939, 3878
The HCF of 7140,3878 is 14.
Lets's calculate GCF of 7140,3878
| 2 | 7140, 3878 |
| 7 | 3570, 1939 |
| 510, 277 |
∴ So the GCF of the given numbers is 2 x 7 = 14
Greatest Common Factor of 7140,3878 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 3878
:1,2,7,14,277,554,1939,3878
Greatest Common Factor
We found the factors 7140,3878 . The biggest common factor number is the GCF number.
So the greatest common factor 7140,3878 is 14.
Lets's calculate LCM of 530,7266
| 2 | 530, 7266 |
| 265, 3633 |
∴ So the LCM of the given numbers is 2 x 265 x 3633 = 1925490
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 14/1925490
Therefore, the GCF of Fractions 7140/530,3878/7266 is 14/1925490
Least Common Multiple of 530,7266 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 530,7266 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(530,7266) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(530,7266) x common factors =2 x 1 = 2
LCM(530,7266) = ( 530 × 7266 ) / 2
LCM(530,7266) = 3850980 / 2
LCM(530,7266) = 1925490
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FAQs on GCF of Fractions of 7140/530, 3878/7266
1. What is the HCF of 7140,3878?
The HCF of 7140,3878 is 14
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 7140/530, 3878/7266?
Answer: GCF of Numerators as per given numbers 7140/530, 3878/7266 is
GCF of Numerators i.e. for 7140,3878 is 14
LCM of denominators i.e. for 530,7266 is 1925490.
Thus, GCF of Fractions is 14/1925490.Finally, GCF of Fractions for 7140/530, 3878/7266 is 14/1925490.