GCF of 3780/313, 9214/7230
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 3780/313, 9214/7230 i.e 2/2262990 easily. The following is the detailed procedure to determine the greatest common factor of fractions 3780/313, 9214/7230.
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 3780/313,9214/7230?
Given fractions are 3780/313,9214/7230
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 3780/313,9214/7230, numerators are 3780,9214
Denominators are 313,7230
The GCF of 3780,9214 is 2 .
LCM of 313,7230 is 2262990.
The greatest common factor of 3780/313,9214/7230 = [GCF of 3780,9214]/[LCM of 313,7230]= 2/2262990
Therefore, the GCF of 3780/313,9214/7230 is 2/2262990.
To find the highest common factor of 3780,9214, we have to find the factors of both numbers and list the highest common factor.
The factors of 3780 are 1, 2, 3, 4, 5, 6, 7, 9, 10, 12, 14, 15, 18, 20, 21, 27, 28, 30, 35, 36, 42, 45, 54, 60, 63, 70, 84, 90, 105, 108, 126, 135, 140, 180, 189, 210, 252, 270, 315, 378, 420, 540, 630, 756, 945, 1260, 1890, 3780
The factors of 9214 are 1, 2, 17, 34, 271, 542, 4607, 9214
The HCF of 3780,9214 is 2.
Lets's calculate GCF of 3780,9214
| 2 | 3780, 9214 |
| 1890, 4607 |
∴ So the GCF of the given numbers is 2 = 2
Greatest Common Factor of 3780,9214 By Matching Biggest Common Factor Method
Now, list down the factors of 3780
:1,2,3,4,5,6,7,9,10,12,14,15,18,20,21,27,28,30,35,36,42,45,54,60,63,70,84,90,105,108,126,135,140,180,189,210,252,270,315,378,420,540,630,756,945,1260,1890,3780
Now, list down the factors of 9214
:1,2,17,34,271,542,4607,9214
Greatest Common Factor
We found the factors 3780,9214 . The biggest common factor number is the GCF number.
So the greatest common factor 3780,9214 is 2.
Lets's calculate LCM of 313,7230
Given numbers has no common factors except 1. So, there LCM is their product i.e 2262990
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/2262990
Therefore, the GCF of Fractions 3780/313,9214/7230 is 2/2262990
Least Common Multiple of 313,7230 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 313,7230 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(313,7230) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(313,7230) x common factors =1 x 1 = 1
LCM(313,7230) = ( 313 × 7230 ) / 1
LCM(313,7230) = 2262990 / 1
LCM(313,7230) = 2262990
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FAQs on GCF of Fractions of 3780/313, 9214/7230
1. What is the HCF of 3780,9214?
The HCF of 3780,9214 is 2
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 3780/313, 9214/7230?
Answer: GCF of Numerators as per given numbers 3780/313, 9214/7230 is
GCF of Numerators i.e. for 3780,9214 is 2
LCM of denominators i.e. for 313,7230 is 2262990.
Thus, GCF of Fractions is 2/2262990.Finally, GCF of Fractions for 3780/313, 9214/7230 is 2/2262990.