Use our free GCF of Fractions Calculator tool to compute the GCF of 54/16, 266/31, 214/748 i.e 2/92752 easily. The following is the detailed procedure to determine the greatest common factor of fractions 54/16, 266/31, 214/748.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 54/16,266/31,214/748
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 54/16,266/31,214/748, numerators are 54,266,214
Denominators are 16,31,748
The GCF of 54,266,214 is 2 .
LCM of 16,31,748 is 92752.
The greatest common factor of 54/16,266/31,214/748 = [GCF of 54,266,214]/[LCM of 16,31,748]= 2/92752
Therefore, the GCF of 54/16,266/31,214/748 is 2/92752.
To find the highest common factor of 54,266,214, 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 266 are 1, 2, 7, 14, 19, 38, 133, 266
The factors of 214 are 1, 2, 107, 214
The HCF of 54,266,214 is 2.
Lets's calculate GCF of 54,266,214
2 | 54, 266, 214 |
27, 133, 107 |
∴ 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 266
:1,2,7,14,19,38,133,266
Now, list down the factors of 214
:1,2,107,214
Greatest Common Factor
We found the factors 54,266,214 . The biggest common factor number is the GCF number.
So the greatest common factor 54,266,214 is 2.
Lets's calculate LCM of 16,31,748
2 | 16, 31, 748 |
2 | 8, 31, 374 |
4, 31, 187 |
∴ So the LCM of the given numbers is 2 x 2 x 4 x 31 x 187 = 92752
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/92752
Therefore, the GCF of Fractions 54/16,266/31,214/748 is 2/92752
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 16,31,748 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(16,31,748) = 1
common factors(in case of two or more numbers have common factors) = 4
GCF(16,31,748) x common factors =1 x 4 = 4
LCM(16,31,748) = ( 16 × 31 × 748 ) / 4
LCM(16,31,748) = 371008 / 4
LCM(16,31,748) = 92752
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 54,266,214?
The HCF of 54,266,214 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 54/16, 266/31, 214/748?
Answer: GCF of Numerators as per given numbers 54/16, 266/31, 214/748 is
GCF of Numerators i.e. for 54,266,214 is 2
LCM of denominators i.e. for 16,31,748 is 92752.
Thus, GCF of Fractions is 2/92752.Finally, GCF of Fractions for 54/16, 266/31, 214/748 is 2/92752.