GCF of 1078/319, 6774/7465
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 1078/319, 6774/7465 i.e 2/2381335 easily. The following is the detailed procedure to determine the greatest common factor of fractions 1078/319, 6774/7465.
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 1078/319,6774/7465?
Given fractions are 1078/319,6774/7465
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 1078/319,6774/7465, numerators are 1078,6774
Denominators are 319,7465
The GCF of 1078,6774 is 2 .
LCM of 319,7465 is 2381335.
The greatest common factor of 1078/319,6774/7465 = [GCF of 1078,6774]/[LCM of 319,7465]= 2/2381335
Therefore, the GCF of 1078/319,6774/7465 is 2/2381335.
To find the highest common factor of 1078,6774, we have to find the factors of both numbers and list the highest common factor.
The factors of 1078 are 1, 2, 7, 11, 14, 22, 49, 77, 98, 154, 539, 1078
The factors of 6774 are 1, 2, 3, 6, 1129, 2258, 3387, 6774
The HCF of 1078,6774 is 2.
Lets's calculate GCF of 1078,6774
| 2 | 1078, 6774 |
| 539, 3387 |
∴ So the GCF of the given numbers is 2 = 2
Greatest Common Factor of 1078,6774 By Matching Biggest Common Factor Method
Now, list down the factors of 1078
:1,2,7,11,14,22,49,77,98,154,539,1078
Now, list down the factors of 6774
:1,2,3,6,1129,2258,3387,6774
Greatest Common Factor
We found the factors 1078,6774 . The biggest common factor number is the GCF number.
So the greatest common factor 1078,6774 is 2.
Lets's calculate LCM of 319,7465
Given numbers has no common factors except 1. So, there LCM is their product i.e 2381335
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/2381335
Therefore, the GCF of Fractions 1078/319,6774/7465 is 2/2381335
Least Common Multiple of 319,7465 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 319,7465 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(319,7465) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(319,7465) x common factors =1 x 1 = 1
LCM(319,7465) = ( 319 × 7465 ) / 1
LCM(319,7465) = 2381335 / 1
LCM(319,7465) = 2381335
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FAQs on GCF of Fractions of 1078/319, 6774/7465
1. What is the HCF of 1078,6774?
The HCF of 1078,6774 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 1078/319, 6774/7465?
Answer: GCF of Numerators as per given numbers 1078/319, 6774/7465 is
GCF of Numerators i.e. for 1078,6774 is 2
LCM of denominators i.e. for 319,7465 is 2381335.
Thus, GCF of Fractions is 2/2381335.Finally, GCF of Fractions for 1078/319, 6774/7465 is 2/2381335.