Use our free GCF of Fractions Calculator tool to compute the GCF of 658/708, 821/334 i.e 1/118236 easily. The following is the detailed procedure to determine the greatest common factor of fractions 658/708, 821/334.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 658/708,821/334
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 658/708,821/334, numerators are 658,821
Denominators are 708,334
The GCF of 658,821 is 1 .
LCM of 708,334 is 118236.
The greatest common factor of 658/708,821/334 = [GCF of 658,821]/[LCM of 708,334]= 1/118236
Therefore, the GCF of 658/708,821/334 is 1/118236.
To find the highest common factor of 658,821, we have to find the factors of both numbers and list the highest common factor.
The factors of 658 are 1, 2, 7, 14, 47, 94, 329, 658
The factors of 821 are 1, 821
The HCF of 658,821 is 1.
Lets's calculate GCF of 658,821
∴ So GCF of numbers is 1 because of no common factors present between them.
Now, list down the factors of 658
:1,2,7,14,47,94,329,658
Now, list down the factors of 821
:1,821
Greatest Common Factor
We found the factors 658,821 . The biggest common factor number is the GCF number.
So the greatest common factor 658,821 is 1.
Lets's calculate LCM of 708,334
2 | 708, 334 |
354, 167 |
∴ So the LCM of the given numbers is 2 x 354 x 167 = 118236
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/118236
Therefore, the GCF of Fractions 658/708,821/334 is 1/118236
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 708,334 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(708,334) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(708,334) x common factors =2 x 1 = 2
LCM(708,334) = ( 708 × 334 ) / 2
LCM(708,334) = 236472 / 2
LCM(708,334) = 118236
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 658,821?
The HCF of 658,821 is 1
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 658/708, 821/334?
Answer: GCF of Numerators as per given numbers 658/708, 821/334 is
GCF of Numerators i.e. for 658,821 is 1
LCM of denominators i.e. for 708,334 is 118236.
Thus, GCF of Fractions is 1/118236.Finally, GCF of Fractions for 658/708, 821/334 is 1/118236.