Use our free GCF of Fractions Calculator tool to compute the GCF of 715/512, 308/842 i.e 11/215552 easily. The following is the detailed procedure to determine the greatest common factor of fractions 715/512, 308/842.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 715/512,308/842
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 715/512,308/842, numerators are 715,308
Denominators are 512,842
The GCF of 715,308 is 11 .
LCM of 512,842 is 215552.
The greatest common factor of 715/512,308/842 = [GCF of 715,308]/[LCM of 512,842]= 11/215552
Therefore, the GCF of 715/512,308/842 is 11/215552.
To find the highest common factor of 715,308, we have to find the factors of both numbers and list the highest common factor.
The factors of 715 are 1, 5, 11, 13, 55, 65, 143, 715
The factors of 308 are 1, 2, 4, 7, 11, 14, 22, 28, 44, 77, 154, 308
The HCF of 715,308 is 11.
Lets's calculate GCF of 715,308
11 | 715, 308 |
65, 28 |
∴ So the GCF of the given numbers is 11 = 11
Now, list down the factors of 715
:1,5,11,13,55,65,143,715
Now, list down the factors of 308
:1,2,4,7,11,14,22,28,44,77,154,308
Greatest Common Factor
We found the factors 715,308 . The biggest common factor number is the GCF number.
So the greatest common factor 715,308 is 11.
Lets's calculate LCM of 512,842
2 | 512, 842 |
256, 421 |
∴ So the LCM of the given numbers is 2 x 256 x 421 = 215552
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 11/215552
Therefore, the GCF of Fractions 715/512,308/842 is 11/215552
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 512,842 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(512,842) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(512,842) x common factors =2 x 1 = 2
LCM(512,842) = ( 512 × 842 ) / 2
LCM(512,842) = 431104 / 2
LCM(512,842) = 215552
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 715,308?
The HCF of 715,308 is 11
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 715/512, 308/842?
Answer: GCF of Numerators as per given numbers 715/512, 308/842 is
GCF of Numerators i.e. for 715,308 is 11
LCM of denominators i.e. for 512,842 is 215552.
Thus, GCF of Fractions is 11/215552.Finally, GCF of Fractions for 715/512, 308/842 is 11/215552.