GCF of 102/309, 2768/840
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 102/309, 2768/840 i.e 2/86520 easily. The following is the detailed procedure to determine the greatest common factor of fractions 102/309, 2768/840.
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 102/309,2768/840?
Given fractions are 102/309,2768/840
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 102/309,2768/840, numerators are 102,2768
Denominators are 309,840
The GCF of 102,2768 is 2 .
LCM of 309,840 is 86520.
The greatest common factor of 102/309,2768/840 = [GCF of 102,2768]/[LCM of 309,840]= 2/86520
Therefore, the GCF of 102/309,2768/840 is 2/86520.
To find the highest common factor of 102,2768, we have to find the factors of both numbers and list the highest common factor.
The factors of 102 are 1, 2, 3, 6, 17, 34, 51, 102
The factors of 2768 are 1, 2, 4, 8, 16, 173, 346, 692, 1384, 2768
The HCF of 102,2768 is 2.
Lets's calculate GCF of 102,2768
| 2 | 102, 2768 |
| 51, 1384 |
∴ So the GCF of the given numbers is 2 = 2
Greatest Common Factor of 102,2768 By Matching Biggest Common Factor Method
Now, list down the factors of 102
:1,2,3,6,17,34,51,102
Now, list down the factors of 2768
:1,2,4,8,16,173,346,692,1384,2768
Greatest Common Factor
We found the factors 102,2768 . The biggest common factor number is the GCF number.
So the greatest common factor 102,2768 is 2.
Lets's calculate LCM of 309,840
| 3 | 309, 840 |
| 103, 280 |
∴ So the LCM of the given numbers is 3 x 103 x 280 = 86520
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/86520
Therefore, the GCF of Fractions 102/309,2768/840 is 2/86520
Least Common Multiple of 309,840 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 309,840 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(309,840) = 3
common factors(in case of two or more numbers have common factors) = 1
GCF(309,840) x common factors =3 x 1 = 3
LCM(309,840) = ( 309 × 840 ) / 3
LCM(309,840) = 259560 / 3
LCM(309,840) = 86520
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FAQs on GCF of Fractions of 102/309, 2768/840
1. What is the HCF of 102,2768?
The HCF of 102,2768 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 102/309, 2768/840?
Answer: GCF of Numerators as per given numbers 102/309, 2768/840 is
GCF of Numerators i.e. for 102,2768 is 2
LCM of denominators i.e. for 309,840 is 86520.
Thus, GCF of Fractions is 2/86520.Finally, GCF of Fractions for 102/309, 2768/840 is 2/86520.