Use our free GCF of Fractions Calculator tool to compute the GCF of 714/908, 314/798 i.e 2/362292 easily. The following is the detailed procedure to determine the greatest common factor of fractions 714/908, 314/798.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 714/908,314/798
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 714/908,314/798, numerators are 714,314
Denominators are 908,798
The GCF of 714,314 is 2 .
LCM of 908,798 is 362292.
The greatest common factor of 714/908,314/798 = [GCF of 714,314]/[LCM of 908,798]= 2/362292
Therefore, the GCF of 714/908,314/798 is 2/362292.
To find the highest common factor of 714,314, 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 314 are 1, 2, 157, 314
The HCF of 714,314 is 2.
Lets's calculate GCF of 714,314
2 | 714, 314 |
357, 157 |
∴ So the GCF of the given numbers is 2 = 2
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 314
:1,2,157,314
Greatest Common Factor
We found the factors 714,314 . The biggest common factor number is the GCF number.
So the greatest common factor 714,314 is 2.
Lets's calculate LCM of 908,798
2 | 908, 798 |
454, 399 |
∴ So the LCM of the given numbers is 2 x 454 x 399 = 362292
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/362292
Therefore, the GCF of Fractions 714/908,314/798 is 2/362292
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 908,798 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(908,798) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(908,798) x common factors =2 x 1 = 2
LCM(908,798) = ( 908 × 798 ) / 2
LCM(908,798) = 724584 / 2
LCM(908,798) = 362292
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 714,314?
The HCF of 714,314 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 714/908, 314/798?
Answer: GCF of Numerators as per given numbers 714/908, 314/798 is
GCF of Numerators i.e. for 714,314 is 2
LCM of denominators i.e. for 908,798 is 362292.
Thus, GCF of Fractions is 2/362292.Finally, GCF of Fractions for 714/908, 314/798 is 2/362292.