Use our free GCF of Fractions Calculator tool to compute the GCF of 798/698, 814/149 i.e 2/104002 easily. The following is the detailed procedure to determine the greatest common factor of fractions 798/698, 814/149.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 798/698,814/149
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 798/698,814/149, numerators are 798,814
Denominators are 698,149
The GCF of 798,814 is 2 .
LCM of 698,149 is 104002.
The greatest common factor of 798/698,814/149 = [GCF of 798,814]/[LCM of 698,149]= 2/104002
Therefore, the GCF of 798/698,814/149 is 2/104002.
To find the highest common factor of 798,814, we have to find the factors of both numbers and list the highest common factor.
The factors of 798 are 1, 2, 3, 6, 7, 14, 19, 21, 38, 42, 57, 114, 133, 266, 399, 798
The factors of 814 are 1, 2, 11, 22, 37, 74, 407, 814
The HCF of 798,814 is 2.
Lets's calculate GCF of 798,814
2 | 798, 814 |
399, 407 |
∴ So the GCF of the given numbers is 2 = 2
Now, list down the factors of 798
:1,2,3,6,7,14,19,21,38,42,57,114,133,266,399,798
Now, list down the factors of 814
:1,2,11,22,37,74,407,814
Greatest Common Factor
We found the factors 798,814 . The biggest common factor number is the GCF number.
So the greatest common factor 798,814 is 2.
Lets's calculate LCM of 698,149
Given numbers has no common factors except 1. So, there LCM is their product i.e 104002
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/104002
Therefore, the GCF of Fractions 798/698,814/149 is 2/104002
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 698,149 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(698,149) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(698,149) x common factors =1 x 1 = 1
LCM(698,149) = ( 698 × 149 ) / 1
LCM(698,149) = 104002 / 1
LCM(698,149) = 104002
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 798,814?
The HCF of 798,814 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 798/698, 814/149?
Answer: GCF of Numerators as per given numbers 798/698, 814/149 is
GCF of Numerators i.e. for 798,814 is 2
LCM of denominators i.e. for 698,149 is 104002.
Thus, GCF of Fractions is 2/104002.Finally, GCF of Fractions for 798/698, 814/149 is 2/104002.