GCF of 218/378, 6224/7658
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 218/378, 6224/7658 i.e 2/206766 easily. The following is the detailed procedure to determine the greatest common factor of fractions 218/378, 6224/7658.
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 218/378,6224/7658?
Given fractions are 218/378,6224/7658
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 218/378,6224/7658, numerators are 218,6224
Denominators are 378,7658
The GCF of 218,6224 is 2 .
LCM of 378,7658 is 206766.
The greatest common factor of 218/378,6224/7658 = [GCF of 218,6224]/[LCM of 378,7658]= 2/206766
Therefore, the GCF of 218/378,6224/7658 is 2/206766.
To find the highest common factor of 218,6224, we have to find the factors of both numbers and list the highest common factor.
The factors of 218 are 1, 2, 109, 218
The factors of 6224 are 1, 2, 4, 8, 16, 389, 778, 1556, 3112, 6224
The HCF of 218,6224 is 2.
Lets's calculate GCF of 218,6224
| 2 | 218, 6224 |
| 109, 3112 |
∴ So the GCF of the given numbers is 2 = 2
Greatest Common Factor of 218,6224 By Matching Biggest Common Factor Method
Now, list down the factors of 218
:1,2,109,218
Now, list down the factors of 6224
:1,2,4,8,16,389,778,1556,3112,6224
Greatest Common Factor
We found the factors 218,6224 . The biggest common factor number is the GCF number.
So the greatest common factor 218,6224 is 2.
Lets's calculate LCM of 378,7658
| 2 | 378, 7658 |
| 7 | 189, 3829 |
| 27, 547 |
∴ So the LCM of the given numbers is 2 x 7 x 27 x 547 = 206766
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/206766
Therefore, the GCF of Fractions 218/378,6224/7658 is 2/206766
Least Common Multiple of 378,7658 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 378,7658 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(378,7658) = 14
common factors(in case of two or more numbers have common factors) = 1
GCF(378,7658) x common factors =14 x 1 = 14
LCM(378,7658) = ( 378 × 7658 ) / 14
LCM(378,7658) = 2894724 / 14
LCM(378,7658) = 206766
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FAQs on GCF of Fractions of 218/378, 6224/7658
1. What is the HCF of 218,6224?
The HCF of 218,6224 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 218/378, 6224/7658?
Answer: GCF of Numerators as per given numbers 218/378, 6224/7658 is
GCF of Numerators i.e. for 218,6224 is 2
LCM of denominators i.e. for 378,7658 is 206766.
Thus, GCF of Fractions is 2/206766.Finally, GCF of Fractions for 218/378, 6224/7658 is 2/206766.