Use our free GCF of Fractions Calculator tool to compute the GCF of 778/973, 310/677 i.e 2/658721 easily. The following is the detailed procedure to determine the greatest common factor of fractions 778/973, 310/677.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 778/973,310/677
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 778/973,310/677, numerators are 778,310
Denominators are 973,677
The GCF of 778,310 is 2 .
LCM of 973,677 is 658721.
The greatest common factor of 778/973,310/677 = [GCF of 778,310]/[LCM of 973,677]= 2/658721
Therefore, the GCF of 778/973,310/677 is 2/658721.
To find the highest common factor of 778,310, we have to find the factors of both numbers and list the highest common factor.
The factors of 778 are 1, 2, 389, 778
The factors of 310 are 1, 2, 5, 10, 31, 62, 155, 310
The HCF of 778,310 is 2.
Lets's calculate GCF of 778,310
2 | 778, 310 |
389, 155 |
∴ So the GCF of the given numbers is 2 = 2
Now, list down the factors of 778
:1,2,389,778
Now, list down the factors of 310
:1,2,5,10,31,62,155,310
Greatest Common Factor
We found the factors 778,310 . The biggest common factor number is the GCF number.
So the greatest common factor 778,310 is 2.
Lets's calculate LCM of 973,677
Given numbers has no common factors except 1. So, there LCM is their product i.e 658721
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/658721
Therefore, the GCF of Fractions 778/973,310/677 is 2/658721
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 973,677 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(973,677) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(973,677) x common factors =1 x 1 = 1
LCM(973,677) = ( 973 × 677 ) / 1
LCM(973,677) = 658721 / 1
LCM(973,677) = 658721
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 778,310?
The HCF of 778,310 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 778/973, 310/677?
Answer: GCF of Numerators as per given numbers 778/973, 310/677 is
GCF of Numerators i.e. for 778,310 is 2
LCM of denominators i.e. for 973,677 is 658721.
Thus, GCF of Fractions is 2/658721.Finally, GCF of Fractions for 778/973, 310/677 is 2/658721.