Use our free GCF of Fractions Calculator tool to compute the GCF of 508/812, 740/684 i.e 4/138852 easily. The following is the detailed procedure to determine the greatest common factor of fractions 508/812, 740/684.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 508/812,740/684
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 508/812,740/684, numerators are 508,740
Denominators are 812,684
The GCF of 508,740 is 4 .
LCM of 812,684 is 138852.
The greatest common factor of 508/812,740/684 = [GCF of 508,740]/[LCM of 812,684]= 4/138852
Therefore, the GCF of 508/812,740/684 is 4/138852.
To find the highest common factor of 508,740, we have to find the factors of both numbers and list the highest common factor.
The factors of 508 are 1, 2, 4, 127, 254, 508
The factors of 740 are 1, 2, 4, 5, 10, 20, 37, 74, 148, 185, 370, 740
The HCF of 508,740 is 4.
Lets's calculate GCF of 508,740
2 | 508, 740 |
2 | 254, 370 |
127, 185 |
∴ So the GCF of the given numbers is 2 x 2 = 4
Now, list down the factors of 508
:1,2,4,127,254,508
Now, list down the factors of 740
:1,2,4,5,10,20,37,74,148,185,370,740
Greatest Common Factor
We found the factors 508,740 . The biggest common factor number is the GCF number.
So the greatest common factor 508,740 is 4.
Lets's calculate LCM of 812,684
2 | 812, 684 |
2 | 406, 342 |
203, 171 |
∴ So the LCM of the given numbers is 2 x 2 x 203 x 171 = 138852
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 4/138852
Therefore, the GCF of Fractions 508/812,740/684 is 4/138852
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 812,684 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(812,684) = 4
common factors(in case of two or more numbers have common factors) = 1
GCF(812,684) x common factors =4 x 1 = 4
LCM(812,684) = ( 812 × 684 ) / 4
LCM(812,684) = 555408 / 4
LCM(812,684) = 138852
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 508,740?
The HCF of 508,740 is 4
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 508/812, 740/684?
Answer: GCF of Numerators as per given numbers 508/812, 740/684 is
GCF of Numerators i.e. for 508,740 is 4
LCM of denominators i.e. for 812,684 is 138852.
Thus, GCF of Fractions is 4/138852.Finally, GCF of Fractions for 508/812, 740/684 is 4/138852.