GCF of 5780/378, 6884/1302
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 5780/378, 6884/1302 i.e 4/11718 easily. The following is the detailed procedure to determine the greatest common factor of fractions 5780/378, 6884/1302.
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 5780/378,6884/1302?
Given fractions are 5780/378,6884/1302
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 5780/378,6884/1302, numerators are 5780,6884
Denominators are 378,1302
The GCF of 5780,6884 is 4 .
LCM of 378,1302 is 11718.
The greatest common factor of 5780/378,6884/1302 = [GCF of 5780,6884]/[LCM of 378,1302]= 4/11718
Therefore, the GCF of 5780/378,6884/1302 is 4/11718.
To find the highest common factor of 5780,6884, we have to find the factors of both numbers and list the highest common factor.
The factors of 5780 are 1, 2, 4, 5, 10, 17, 20, 34, 68, 85, 170, 289, 340, 578, 1156, 1445, 2890, 5780
The factors of 6884 are 1, 2, 4, 1721, 3442, 6884
The HCF of 5780,6884 is 4.
Lets's calculate GCF of 5780,6884
| 2 | 5780, 6884 |
| 2 | 2890, 3442 |
| 1445, 1721 |
∴ So the GCF of the given numbers is 2 x 2 = 4
Greatest Common Factor of 5780,6884 By Matching Biggest Common Factor Method
Now, list down the factors of 5780
:1,2,4,5,10,17,20,34,68,85,170,289,340,578,1156,1445,2890,5780
Now, list down the factors of 6884
:1,2,4,1721,3442,6884
Greatest Common Factor
We found the factors 5780,6884 . The biggest common factor number is the GCF number.
So the greatest common factor 5780,6884 is 4.
Lets's calculate LCM of 378,1302
| 2 | 378, 1302 |
| 3 | 189, 651 |
| 7 | 63, 217 |
| 9, 31 |
∴ So the LCM of the given numbers is 2 x 3 x 7 x 9 x 31 = 11718
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 4/11718
Therefore, the GCF of Fractions 5780/378,6884/1302 is 4/11718
Least Common Multiple of 378,1302 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 378,1302 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(378,1302) = 42
common factors(in case of two or more numbers have common factors) = 1
GCF(378,1302) x common factors =42 x 1 = 42
LCM(378,1302) = ( 378 × 1302 ) / 42
LCM(378,1302) = 492156 / 42
LCM(378,1302) = 11718
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FAQs on GCF of Fractions of 5780/378, 6884/1302
1. What is the HCF of 5780,6884?
The HCF of 5780,6884 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 5780/378, 6884/1302?
Answer: GCF of Numerators as per given numbers 5780/378, 6884/1302 is
GCF of Numerators i.e. for 5780,6884 is 4
LCM of denominators i.e. for 378,1302 is 11718.
Thus, GCF of Fractions is 4/11718.Finally, GCF of Fractions for 5780/378, 6884/1302 is 4/11718.