Use our free GCF of Fractions Calculator tool to compute the GCF of 680/472, 345/348 i.e 5/41064 easily. The following is the detailed procedure to determine the greatest common factor of fractions 680/472, 345/348.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 680/472,345/348
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 680/472,345/348, numerators are 680,345
Denominators are 472,348
The GCF of 680,345 is 5 .
LCM of 472,348 is 41064.
The greatest common factor of 680/472,345/348 = [GCF of 680,345]/[LCM of 472,348]= 5/41064
Therefore, the GCF of 680/472,345/348 is 5/41064.
To find the highest common factor of 680,345, we have to find the factors of both numbers and list the highest common factor.
The factors of 680 are 1, 2, 4, 5, 8, 10, 17, 20, 34, 40, 68, 85, 136, 170, 340, 680
The factors of 345 are 1, 3, 5, 15, 23, 69, 115, 345
The HCF of 680,345 is 5.
Lets's calculate GCF of 680,345
5 | 680, 345 |
136, 69 |
∴ So the GCF of the given numbers is 5 = 5
Now, list down the factors of 680
:1,2,4,5,8,10,17,20,34,40,68,85,136,170,340,680
Now, list down the factors of 345
:1,3,5,15,23,69,115,345
Greatest Common Factor
We found the factors 680,345 . The biggest common factor number is the GCF number.
So the greatest common factor 680,345 is 5.
Lets's calculate LCM of 472,348
2 | 472, 348 |
2 | 236, 174 |
118, 87 |
∴ So the LCM of the given numbers is 2 x 2 x 118 x 87 = 41064
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 5/41064
Therefore, the GCF of Fractions 680/472,345/348 is 5/41064
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 472,348 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(472,348) = 4
common factors(in case of two or more numbers have common factors) = 1
GCF(472,348) x common factors =4 x 1 = 4
LCM(472,348) = ( 472 × 348 ) / 4
LCM(472,348) = 164256 / 4
LCM(472,348) = 41064
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 680,345?
The HCF of 680,345 is 5
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 680/472, 345/348?
Answer: GCF of Numerators as per given numbers 680/472, 345/348 is
GCF of Numerators i.e. for 680,345 is 5
LCM of denominators i.e. for 472,348 is 41064.
Thus, GCF of Fractions is 5/41064.Finally, GCF of Fractions for 680/472, 345/348 is 5/41064.