GCF of 778/230, 7678/278
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 778/230, 7678/278 i.e 2/31970 easily. The following is the detailed procedure to determine the greatest common factor of fractions 778/230, 7678/278.
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 778/230,7678/278?
Given fractions are 778/230,7678/278
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 778/230,7678/278, numerators are 778,7678
Denominators are 230,278
The GCF of 778,7678 is 2 .
LCM of 230,278 is 31970.
The greatest common factor of 778/230,7678/278 = [GCF of 778,7678]/[LCM of 230,278]= 2/31970
Therefore, the GCF of 778/230,7678/278 is 2/31970.
To find the highest common factor of 778,7678, we have to find the factors of both numbers and list the highest common factor.
The factors of 778 are 1, 2, 389, 778
The factors of 7678 are 1, 2, 11, 22, 349, 698, 3839, 7678
The HCF of 778,7678 is 2.
Lets's calculate GCF of 778,7678
| 2 | 778, 7678 |
| 389, 3839 |
∴ So the GCF of the given numbers is 2 = 2
Greatest Common Factor of 778,7678 By Matching Biggest Common Factor Method
Now, list down the factors of 778
:1,2,389,778
Now, list down the factors of 7678
:1,2,11,22,349,698,3839,7678
Greatest Common Factor
We found the factors 778,7678 . The biggest common factor number is the GCF number.
So the greatest common factor 778,7678 is 2.
Lets's calculate LCM of 230,278
| 2 | 230, 278 |
| 115, 139 |
∴ So the LCM of the given numbers is 2 x 115 x 139 = 31970
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/31970
Therefore, the GCF of Fractions 778/230,7678/278 is 2/31970
Least Common Multiple of 230,278 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 230,278 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(230,278) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(230,278) x common factors =2 x 1 = 2
LCM(230,278) = ( 230 × 278 ) / 2
LCM(230,278) = 63940 / 2
LCM(230,278) = 31970
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FAQs on GCF of Fractions of 778/230, 7678/278
1. What is the HCF of 778,7678?
The HCF of 778,7678 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 778/230, 7678/278?
Answer: GCF of Numerators as per given numbers 778/230, 7678/278 is
GCF of Numerators i.e. for 778,7678 is 2
LCM of denominators i.e. for 230,278 is 31970.
Thus, GCF of Fractions is 2/31970.Finally, GCF of Fractions for 778/230, 7678/278 is 2/31970.