Use our free GCF of Fractions Calculator tool to compute the GCF of 308/214, 510/432 i.e 2/46224 easily. The following is the detailed procedure to determine the greatest common factor of fractions 308/214, 510/432.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 308/214,510/432
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 308/214,510/432, numerators are 308,510
Denominators are 214,432
The GCF of 308,510 is 2 .
LCM of 214,432 is 46224.
The greatest common factor of 308/214,510/432 = [GCF of 308,510]/[LCM of 214,432]= 2/46224
Therefore, the GCF of 308/214,510/432 is 2/46224.
To find the highest common factor of 308,510, we have to find the factors of both numbers and list the highest common factor.
The factors of 308 are 1, 2, 4, 7, 11, 14, 22, 28, 44, 77, 154, 308
The factors of 510 are 1, 2, 3, 5, 6, 10, 15, 17, 30, 34, 51, 85, 102, 170, 255, 510
The HCF of 308,510 is 2.
Lets's calculate GCF of 308,510
2 | 308, 510 |
154, 255 |
∴ So the GCF of the given numbers is 2 = 2
Now, list down the factors of 308
:1,2,4,7,11,14,22,28,44,77,154,308
Now, list down the factors of 510
:1,2,3,5,6,10,15,17,30,34,51,85,102,170,255,510
Greatest Common Factor
We found the factors 308,510 . The biggest common factor number is the GCF number.
So the greatest common factor 308,510 is 2.
Lets's calculate LCM of 214,432
2 | 214, 432 |
107, 216 |
∴ So the LCM of the given numbers is 2 x 107 x 216 = 46224
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/46224
Therefore, the GCF of Fractions 308/214,510/432 is 2/46224
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 214,432 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(214,432) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(214,432) x common factors =2 x 1 = 2
LCM(214,432) = ( 214 × 432 ) / 2
LCM(214,432) = 92448 / 2
LCM(214,432) = 46224
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 308,510?
The HCF of 308,510 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 308/214, 510/432?
Answer: GCF of Numerators as per given numbers 308/214, 510/432 is
GCF of Numerators i.e. for 308,510 is 2
LCM of denominators i.e. for 214,432 is 46224.
Thus, GCF of Fractions is 2/46224.Finally, GCF of Fractions for 308/214, 510/432 is 2/46224.