Use our free GCF of Fractions Calculator tool to compute the GCF of 54/34, 80/172, 684/229 i.e 2/669596 easily. The following is the detailed procedure to determine the greatest common factor of fractions 54/34, 80/172, 684/229.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 54/34,80/172,684/229
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 54/34,80/172,684/229, numerators are 54,80,684
Denominators are 34,172,229
The GCF of 54,80,684 is 2 .
LCM of 34,172,229 is 669596.
The greatest common factor of 54/34,80/172,684/229 = [GCF of 54,80,684]/[LCM of 34,172,229]= 2/669596
Therefore, the GCF of 54/34,80/172,684/229 is 2/669596.
To find the highest common factor of 54,80,684, we have to find the factors of both numbers and list the highest common factor.
The factors of 54 are 1, 2, 3, 6, 9, 18, 27, 54
The factors of 80 are 1, 2, 4, 5, 8, 10, 16, 20, 40, 80
The factors of 684 are 1, 2, 3, 4, 6, 9, 12, 18, 19, 36, 38, 57, 76, 114, 171, 228, 342, 684
The HCF of 54,80,684 is 2.
Lets's calculate GCF of 54,80,684
2 | 54, 80, 684 |
27, 40, 342 |
∴ So the GCF of the given numbers is 2 = 2
Now, list down the factors of 54
:1,2,3,6,9,18,27,54
Now, list down the factors of 80
:1,2,4,5,8,10,16,20,40,80
Now, list down the factors of 684
:1,2,3,4,6,9,12,18,19,36,38,57,76,114,171,228,342,684
Greatest Common Factor
We found the factors 54,80,684 . The biggest common factor number is the GCF number.
So the greatest common factor 54,80,684 is 2.
Lets's calculate LCM of 34,172,229
2 | 34, 172, 229 |
17, 86, 229 |
∴ So the LCM of the given numbers is 2 x 17 x 86 x 229 = 669596
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/669596
Therefore, the GCF of Fractions 54/34,80/172,684/229 is 2/669596
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 34,172,229 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(34,172,229) = 1
common factors(in case of two or more numbers have common factors) = 2
GCF(34,172,229) x common factors =1 x 2 = 2
LCM(34,172,229) = ( 34 × 172 × 229 ) / 2
LCM(34,172,229) = 1339192 / 2
LCM(34,172,229) = 669596
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 54,80,684?
The HCF of 54,80,684 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 54/34, 80/172, 684/229?
Answer: GCF of Numerators as per given numbers 54/34, 80/172, 684/229 is
GCF of Numerators i.e. for 54,80,684 is 2
LCM of denominators i.e. for 34,172,229 is 669596.
Thus, GCF of Fractions is 2/669596.Finally, GCF of Fractions for 54/34, 80/172, 684/229 is 2/669596.