Use our free GCF of Fractions Calculator tool to compute the GCF of 714/546, 832/249 i.e 2/45318 easily. The following is the detailed procedure to determine the greatest common factor of fractions 714/546, 832/249.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 714/546,832/249
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 714/546,832/249, numerators are 714,832
Denominators are 546,249
The GCF of 714,832 is 2 .
LCM of 546,249 is 45318.
The greatest common factor of 714/546,832/249 = [GCF of 714,832]/[LCM of 546,249]= 2/45318
Therefore, the GCF of 714/546,832/249 is 2/45318.
To find the highest common factor of 714,832, we have to find the factors of both numbers and list the highest common factor.
The factors of 714 are 1, 2, 3, 6, 7, 14, 17, 21, 34, 42, 51, 102, 119, 238, 357, 714
The factors of 832 are 1, 2, 4, 8, 13, 16, 26, 32, 52, 64, 104, 208, 416, 832
The HCF of 714,832 is 2.
Lets's calculate GCF of 714,832
2 | 714, 832 |
357, 416 |
∴ So the GCF of the given numbers is 2 = 2
Now, list down the factors of 714
:1,2,3,6,7,14,17,21,34,42,51,102,119,238,357,714
Now, list down the factors of 832
:1,2,4,8,13,16,26,32,52,64,104,208,416,832
Greatest Common Factor
We found the factors 714,832 . The biggest common factor number is the GCF number.
So the greatest common factor 714,832 is 2.
Lets's calculate LCM of 546,249
3 | 546, 249 |
182, 83 |
∴ So the LCM of the given numbers is 3 x 182 x 83 = 45318
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/45318
Therefore, the GCF of Fractions 714/546,832/249 is 2/45318
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 546,249 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(546,249) = 3
common factors(in case of two or more numbers have common factors) = 1
GCF(546,249) x common factors =3 x 1 = 3
LCM(546,249) = ( 546 × 249 ) / 3
LCM(546,249) = 135954 / 3
LCM(546,249) = 45318
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 714,832?
The HCF of 714,832 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 714/546, 832/249?
Answer: GCF of Numerators as per given numbers 714/546, 832/249 is
GCF of Numerators i.e. for 714,832 is 2
LCM of denominators i.e. for 546,249 is 45318.
Thus, GCF of Fractions is 2/45318.Finally, GCF of Fractions for 714/546, 832/249 is 2/45318.