GCF of 8960/306, 7210/321
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 8960/306, 7210/321 i.e 70/32742 easily. The following is the detailed procedure to determine the greatest common factor of fractions 8960/306, 7210/321.
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 8960/306,7210/321?
Given fractions are 8960/306,7210/321
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 8960/306,7210/321, numerators are 8960,7210
Denominators are 306,321
The GCF of 8960,7210 is 70 .
LCM of 306,321 is 32742.
The greatest common factor of 8960/306,7210/321 = [GCF of 8960,7210]/[LCM of 306,321]= 70/32742
Therefore, the GCF of 8960/306,7210/321 is 70/32742.
To find the highest common factor of 8960,7210, we have to find the factors of both numbers and list the highest common factor.
The factors of 8960 are 1, 2, 4, 5, 7, 8, 10, 14, 16, 20, 28, 32, 35, 40, 56, 64, 70, 80, 112, 128, 140, 160, 224, 256, 280, 320, 448, 560, 640, 896, 1120, 1280, 1792, 2240, 4480, 8960
The factors of 7210 are 1, 2, 5, 7, 10, 14, 35, 70, 103, 206, 515, 721, 1030, 1442, 3605, 7210
The HCF of 8960,7210 is 70.
Lets's calculate GCF of 8960,7210
| 2 | 8960, 7210 |
| 5 | 4480, 3605 |
| 7 | 896, 721 |
| 128, 103 |
∴ So the GCF of the given numbers is 2 x 5 x 7 = 70
Greatest Common Factor of 8960,7210 By Matching Biggest Common Factor Method
Now, list down the factors of 8960
:1,2,4,5,7,8,10,14,16,20,28,32,35,40,56,64,70,80,112,128,140,160,224,256,280,320,448,560,640,896,1120,1280,1792,2240,4480,8960
Now, list down the factors of 7210
:1,2,5,7,10,14,35,70,103,206,515,721,1030,1442,3605,7210
Greatest Common Factor
We found the factors 8960,7210 . The biggest common factor number is the GCF number.
So the greatest common factor 8960,7210 is 70.
Lets's calculate LCM of 306,321
| 3 | 306, 321 |
| 102, 107 |
∴ So the LCM of the given numbers is 3 x 102 x 107 = 32742
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 70/32742
Therefore, the GCF of Fractions 8960/306,7210/321 is 70/32742
Least Common Multiple of 306,321 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 306,321 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(306,321) = 3
common factors(in case of two or more numbers have common factors) = 1
GCF(306,321) x common factors =3 x 1 = 3
LCM(306,321) = ( 306 × 321 ) / 3
LCM(306,321) = 98226 / 3
LCM(306,321) = 32742
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FAQs on GCF of Fractions of 8960/306, 7210/321
1. What is the HCF of 8960,7210?
The HCF of 8960,7210 is 70
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 8960/306, 7210/321?
Answer: GCF of Numerators as per given numbers 8960/306, 7210/321 is
GCF of Numerators i.e. for 8960,7210 is 70
LCM of denominators i.e. for 306,321 is 32742.
Thus, GCF of Fractions is 70/32742.Finally, GCF of Fractions for 8960/306, 7210/321 is 70/32742.