Use our free GCF of Fractions Calculator tool to compute the GCF of 676/304, 975/684 i.e 13/2736 easily. The following is the detailed procedure to determine the greatest common factor of fractions 676/304, 975/684.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 676/304,975/684
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 676/304,975/684, numerators are 676,975
Denominators are 304,684
The GCF of 676,975 is 13 .
LCM of 304,684 is 2736.
The greatest common factor of 676/304,975/684 = [GCF of 676,975]/[LCM of 304,684]= 13/2736
Therefore, the GCF of 676/304,975/684 is 13/2736.
To find the highest common factor of 676,975, we have to find the factors of both numbers and list the highest common factor.
The factors of 676 are 1, 2, 4, 13, 26, 52, 169, 338, 676
The factors of 975 are 1, 3, 5, 13, 15, 25, 39, 65, 75, 195, 325, 975
The HCF of 676,975 is 13.
Lets's calculate GCF of 676,975
13 | 676, 975 |
52, 75 |
∴ So the GCF of the given numbers is 13 = 13
Now, list down the factors of 676
:1,2,4,13,26,52,169,338,676
Now, list down the factors of 975
:1,3,5,13,15,25,39,65,75,195,325,975
Greatest Common Factor
We found the factors 676,975 . The biggest common factor number is the GCF number.
So the greatest common factor 676,975 is 13.
Lets's calculate LCM of 304,684
2 | 304, 684 |
2 | 152, 342 |
19 | 76, 171 |
4, 9 |
∴ So the LCM of the given numbers is 2 x 2 x 19 x 4 x 9 = 2736
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 13/2736
Therefore, the GCF of Fractions 676/304,975/684 is 13/2736
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 304,684 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(304,684) = 76
common factors(in case of two or more numbers have common factors) = 1
GCF(304,684) x common factors =76 x 1 = 76
LCM(304,684) = ( 304 × 684 ) / 76
LCM(304,684) = 207936 / 76
LCM(304,684) = 2736
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 676,975?
The HCF of 676,975 is 13
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 676/304, 975/684?
Answer: GCF of Numerators as per given numbers 676/304, 975/684 is
GCF of Numerators i.e. for 676,975 is 13
LCM of denominators i.e. for 304,684 is 2736.
Thus, GCF of Fractions is 13/2736.Finally, GCF of Fractions for 676/304, 975/684 is 13/2736.