Use our free GCF of Fractions Calculator tool to compute the GCF of 714/474, 594/771 i.e 6/121818 easily. The following is the detailed procedure to determine the greatest common factor of fractions 714/474, 594/771.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 714/474,594/771
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 714/474,594/771, numerators are 714,594
Denominators are 474,771
The GCF of 714,594 is 6 .
LCM of 474,771 is 121818.
The greatest common factor of 714/474,594/771 = [GCF of 714,594]/[LCM of 474,771]= 6/121818
Therefore, the GCF of 714/474,594/771 is 6/121818.
To find the highest common factor of 714,594, we have to find the factors of both numbers and list the highest common factor.
The factors of 714 are 1, 2, 3, 6, 7, 14, 17, 21, 34, 42, 51, 102, 119, 238, 357, 714
The factors of 594 are 1, 2, 3, 6, 9, 11, 18, 22, 27, 33, 54, 66, 99, 198, 297, 594
The HCF of 714,594 is 6.
Lets's calculate GCF of 714,594
2 | 714, 594 |
3 | 357, 297 |
119, 99 |
∴ So the GCF of the given numbers is 2 x 3 = 6
Now, list down the factors of 714
:1,2,3,6,7,14,17,21,34,42,51,102,119,238,357,714
Now, list down the factors of 594
:1,2,3,6,9,11,18,22,27,33,54,66,99,198,297,594
Greatest Common Factor
We found the factors 714,594 . The biggest common factor number is the GCF number.
So the greatest common factor 714,594 is 6.
Lets's calculate LCM of 474,771
3 | 474, 771 |
158, 257 |
∴ So the LCM of the given numbers is 3 x 158 x 257 = 121818
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 6/121818
Therefore, the GCF of Fractions 714/474,594/771 is 6/121818
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 474,771 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(474,771) = 3
common factors(in case of two or more numbers have common factors) = 1
GCF(474,771) x common factors =3 x 1 = 3
LCM(474,771) = ( 474 × 771 ) / 3
LCM(474,771) = 365454 / 3
LCM(474,771) = 121818
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 714,594?
The HCF of 714,594 is 6
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 714/474, 594/771?
Answer: GCF of Numerators as per given numbers 714/474, 594/771 is
GCF of Numerators i.e. for 714,594 is 6
LCM of denominators i.e. for 474,771 is 121818.
Thus, GCF of Fractions is 6/121818.Finally, GCF of Fractions for 714/474, 594/771 is 6/121818.