Use our free GCF of Fractions Calculator tool to compute the GCF of 712/239, 508/278 i.e 4/66442 easily. The following is the detailed procedure to determine the greatest common factor of fractions 712/239, 508/278.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 712/239,508/278
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 712/239,508/278, numerators are 712,508
Denominators are 239,278
The GCF of 712,508 is 4 .
LCM of 239,278 is 66442.
The greatest common factor of 712/239,508/278 = [GCF of 712,508]/[LCM of 239,278]= 4/66442
Therefore, the GCF of 712/239,508/278 is 4/66442.
To find the highest common factor of 712,508, we have to find the factors of both numbers and list the highest common factor.
The factors of 712 are 1, 2, 4, 8, 89, 178, 356, 712
The factors of 508 are 1, 2, 4, 127, 254, 508
The HCF of 712,508 is 4.
Lets's calculate GCF of 712,508
2 | 712, 508 |
2 | 356, 254 |
178, 127 |
∴ So the GCF of the given numbers is 2 x 2 = 4
Now, list down the factors of 712
:1,2,4,8,89,178,356,712
Now, list down the factors of 508
:1,2,4,127,254,508
Greatest Common Factor
We found the factors 712,508 . The biggest common factor number is the GCF number.
So the greatest common factor 712,508 is 4.
Lets's calculate LCM of 239,278
Given numbers has no common factors except 1. So, there LCM is their product i.e 66442
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 4/66442
Therefore, the GCF of Fractions 712/239,508/278 is 4/66442
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 239,278 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(239,278) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(239,278) x common factors =1 x 1 = 1
LCM(239,278) = ( 239 × 278 ) / 1
LCM(239,278) = 66442 / 1
LCM(239,278) = 66442
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 712,508?
The HCF of 712,508 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 712/239, 508/278?
Answer: GCF of Numerators as per given numbers 712/239, 508/278 is
GCF of Numerators i.e. for 712,508 is 4
LCM of denominators i.e. for 239,278 is 66442.
Thus, GCF of Fractions is 4/66442.Finally, GCF of Fractions for 712/239, 508/278 is 4/66442.