GCF of 6840/212, 7676/6857
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 6840/212, 7676/6857 i.e 76/1453684 easily. The following is the detailed procedure to determine the greatest common factor of fractions 6840/212, 7676/6857.
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 6840/212,7676/6857?
Given fractions are 6840/212,7676/6857
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 6840/212,7676/6857, numerators are 6840,7676
Denominators are 212,6857
The GCF of 6840,7676 is 76 .
LCM of 212,6857 is 1453684.
The greatest common factor of 6840/212,7676/6857 = [GCF of 6840,7676]/[LCM of 212,6857]= 76/1453684
Therefore, the GCF of 6840/212,7676/6857 is 76/1453684.
To find the highest common factor of 6840,7676, we have to find the factors of both numbers and list the highest common factor.
The factors of 6840 are 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 19, 20, 24, 30, 36, 38, 40, 45, 57, 60, 72, 76, 90, 95, 114, 120, 152, 171, 180, 190, 228, 285, 342, 360, 380, 456, 570, 684, 760, 855, 1140, 1368, 1710, 2280, 3420, 6840
The factors of 7676 are 1, 2, 4, 19, 38, 76, 101, 202, 404, 1919, 3838, 7676
The HCF of 6840,7676 is 76.
Lets's calculate GCF of 6840,7676
| 2 | 6840, 7676 |
| 2 | 3420, 3838 |
| 19 | 1710, 1919 |
| 90, 101 |
∴ So the GCF of the given numbers is 2 x 2 x 19 = 76
Greatest Common Factor of 6840,7676 By Matching Biggest Common Factor Method
Now, list down the factors of 6840
:1,2,3,4,5,6,8,9,10,12,15,18,19,20,24,30,36,38,40,45,57,60,72,76,90,95,114,120,152,171,180,190,228,285,342,360,380,456,570,684,760,855,1140,1368,1710,2280,3420,6840
Now, list down the factors of 7676
:1,2,4,19,38,76,101,202,404,1919,3838,7676
Greatest Common Factor
We found the factors 6840,7676 . The biggest common factor number is the GCF number.
So the greatest common factor 6840,7676 is 76.
Lets's calculate LCM of 212,6857
Given numbers has no common factors except 1. So, there LCM is their product i.e 1453684
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 76/1453684
Therefore, the GCF of Fractions 6840/212,7676/6857 is 76/1453684
Least Common Multiple of 212,6857 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 212,6857 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(212,6857) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(212,6857) x common factors =1 x 1 = 1
LCM(212,6857) = ( 212 × 6857 ) / 1
LCM(212,6857) = 1453684 / 1
LCM(212,6857) = 1453684
GCF of Fractions Calculation Examples
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FAQs on GCF of Fractions of 6840/212, 7676/6857
1. What is the HCF of 6840,7676?
The HCF of 6840,7676 is 76
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 6840/212, 7676/6857?
Answer: GCF of Numerators as per given numbers 6840/212, 7676/6857 is
GCF of Numerators i.e. for 6840,7676 is 76
LCM of denominators i.e. for 212,6857 is 1453684.
Thus, GCF of Fractions is 76/1453684.Finally, GCF of Fractions for 6840/212, 7676/6857 is 76/1453684.