GCF of 7770/780, 3114/7407
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 7770/780, 3114/7407 i.e 6/1925820 easily. The following is the detailed procedure to determine the greatest common factor of fractions 7770/780, 3114/7407.
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 7770/780,3114/7407?
Given fractions are 7770/780,3114/7407
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 7770/780,3114/7407, numerators are 7770,3114
Denominators are 780,7407
The GCF of 7770,3114 is 6 .
LCM of 780,7407 is 1925820.
The greatest common factor of 7770/780,3114/7407 = [GCF of 7770,3114]/[LCM of 780,7407]= 6/1925820
Therefore, the GCF of 7770/780,3114/7407 is 6/1925820.
To find the highest common factor of 7770,3114, we have to find the factors of both numbers and list the highest common factor.
The factors of 7770 are 1, 2, 3, 5, 6, 7, 10, 14, 15, 21, 30, 35, 37, 42, 70, 74, 105, 111, 185, 210, 222, 259, 370, 518, 555, 777, 1110, 1295, 1554, 2590, 3885, 7770
The factors of 3114 are 1, 2, 3, 6, 9, 18, 173, 346, 519, 1038, 1557, 3114
The HCF of 7770,3114 is 6.
Lets's calculate GCF of 7770,3114
| 2 | 7770, 3114 |
| 3 | 3885, 1557 |
| 1295, 519 |
∴ So the GCF of the given numbers is 2 x 3 = 6
Greatest Common Factor of 7770,3114 By Matching Biggest Common Factor Method
Now, list down the factors of 7770
:1,2,3,5,6,7,10,14,15,21,30,35,37,42,70,74,105,111,185,210,222,259,370,518,555,777,1110,1295,1554,2590,3885,7770
Now, list down the factors of 3114
:1,2,3,6,9,18,173,346,519,1038,1557,3114
Greatest Common Factor
We found the factors 7770,3114 . The biggest common factor number is the GCF number.
So the greatest common factor 7770,3114 is 6.
Lets's calculate LCM of 780,7407
| 3 | 780, 7407 |
| 260, 2469 |
∴ So the LCM of the given numbers is 3 x 260 x 2469 = 1925820
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 6/1925820
Therefore, the GCF of Fractions 7770/780,3114/7407 is 6/1925820
Least Common Multiple of 780,7407 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 780,7407 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(780,7407) = 3
common factors(in case of two or more numbers have common factors) = 1
GCF(780,7407) x common factors =3 x 1 = 3
LCM(780,7407) = ( 780 × 7407 ) / 3
LCM(780,7407) = 5777460 / 3
LCM(780,7407) = 1925820
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FAQs on GCF of Fractions of 7770/780, 3114/7407
1. What is the HCF of 7770,3114?
The HCF of 7770,3114 is 6
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 7770/780, 3114/7407?
Answer: GCF of Numerators as per given numbers 7770/780, 3114/7407 is
GCF of Numerators i.e. for 7770,3114 is 6
LCM of denominators i.e. for 780,7407 is 1925820.
Thus, GCF of Fractions is 6/1925820.Finally, GCF of Fractions for 7770/780, 3114/7407 is 6/1925820.