GCF of 3219/778, 6178/7706
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 3219/778, 6178/7706 i.e 1/2997634 easily. The following is the detailed procedure to determine the greatest common factor of fractions 3219/778, 6178/7706.
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 3219/778,6178/7706?
Given fractions are 3219/778,6178/7706
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 3219/778,6178/7706, numerators are 3219,6178
Denominators are 778,7706
The GCF of 3219,6178 is 1 .
LCM of 778,7706 is 2997634.
The greatest common factor of 3219/778,6178/7706 = [GCF of 3219,6178]/[LCM of 778,7706]= 1/2997634
Therefore, the GCF of 3219/778,6178/7706 is 1/2997634.
To find the highest common factor of 3219,6178, we have to find the factors of both numbers and list the highest common factor.
The factors of 3219 are 1, 3, 29, 37, 87, 111, 1073, 3219
The factors of 6178 are 1, 2, 3089, 6178
The HCF of 3219,6178 is 1.
Lets's calculate GCF of 3219,6178
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 3219,6178 By Matching Biggest Common Factor Method
Now, list down the factors of 3219
:1,3,29,37,87,111,1073,3219
Now, list down the factors of 6178
:1,2,3089,6178
Greatest Common Factor
We found the factors 3219,6178 . The biggest common factor number is the GCF number.
So the greatest common factor 3219,6178 is 1.
Lets's calculate LCM of 778,7706
| 2 | 778, 7706 |
| 389, 3853 |
∴ So the LCM of the given numbers is 2 x 389 x 3853 = 2997634
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/2997634
Therefore, the GCF of Fractions 3219/778,6178/7706 is 1/2997634
Least Common Multiple of 778,7706 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 778,7706 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(778,7706) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(778,7706) x common factors =2 x 1 = 2
LCM(778,7706) = ( 778 × 7706 ) / 2
LCM(778,7706) = 5995268 / 2
LCM(778,7706) = 2997634
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FAQs on GCF of Fractions of 3219/778, 6178/7706
1. What is the HCF of 3219,6178?
The HCF of 3219,6178 is 1
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 3219/778, 6178/7706?
Answer: GCF of Numerators as per given numbers 3219/778, 6178/7706 is
GCF of Numerators i.e. for 3219,6178 is 1
LCM of denominators i.e. for 778,7706 is 2997634.
Thus, GCF of Fractions is 1/2997634.Finally, GCF of Fractions for 3219/778, 6178/7706 is 1/2997634.