Use our free GCF of Fractions Calculator tool to compute the GCF of 814/56, 306/758 i.e 2/21224 easily. The following is the detailed procedure to determine the greatest common factor of fractions 814/56, 306/758.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 814/56,306/758
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 814/56,306/758, numerators are 814,306
Denominators are 56,758
The GCF of 814,306 is 2 .
LCM of 56,758 is 21224.
The greatest common factor of 814/56,306/758 = [GCF of 814,306]/[LCM of 56,758]= 2/21224
Therefore, the GCF of 814/56,306/758 is 2/21224.
To find the highest common factor of 814,306, we have to find the factors of both numbers and list the highest common factor.
The factors of 814 are 1, 2, 11, 22, 37, 74, 407, 814
The factors of 306 are 1, 2, 3, 6, 9, 17, 18, 34, 51, 102, 153, 306
The HCF of 814,306 is 2.
Lets's calculate GCF of 814,306
2 | 814, 306 |
407, 153 |
∴ So the GCF of the given numbers is 2 = 2
Now, list down the factors of 814
:1,2,11,22,37,74,407,814
Now, list down the factors of 306
:1,2,3,6,9,17,18,34,51,102,153,306
Greatest Common Factor
We found the factors 814,306 . The biggest common factor number is the GCF number.
So the greatest common factor 814,306 is 2.
Lets's calculate LCM of 56,758
2 | 56, 758 |
28, 379 |
∴ So the LCM of the given numbers is 2 x 28 x 379 = 21224
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/21224
Therefore, the GCF of Fractions 814/56,306/758 is 2/21224
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 56,758 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(56,758) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(56,758) x common factors =2 x 1 = 2
LCM(56,758) = ( 56 × 758 ) / 2
LCM(56,758) = 42448 / 2
LCM(56,758) = 21224
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 814,306?
The HCF of 814,306 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 814/56, 306/758?
Answer: GCF of Numerators as per given numbers 814/56, 306/758 is
GCF of Numerators i.e. for 814,306 is 2
LCM of denominators i.e. for 56,758 is 21224.
Thus, GCF of Fractions is 2/21224.Finally, GCF of Fractions for 814/56, 306/758 is 2/21224.