Use our free GCF of Fractions Calculator tool to compute the GCF of 778/123, 686/400 i.e 2/49200 easily. The following is the detailed procedure to determine the greatest common factor of fractions 778/123, 686/400.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 778/123,686/400
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 778/123,686/400, numerators are 778,686
Denominators are 123,400
The GCF of 778,686 is 2 .
LCM of 123,400 is 49200.
The greatest common factor of 778/123,686/400 = [GCF of 778,686]/[LCM of 123,400]= 2/49200
Therefore, the GCF of 778/123,686/400 is 2/49200.
To find the highest common factor of 778,686, 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 686 are 1, 2, 7, 14, 49, 98, 343, 686
The HCF of 778,686 is 2.
Lets's calculate GCF of 778,686
2 | 778, 686 |
389, 343 |
∴ 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 686
:1,2,7,14,49,98,343,686
Greatest Common Factor
We found the factors 778,686 . The biggest common factor number is the GCF number.
So the greatest common factor 778,686 is 2.
Lets's calculate LCM of 123,400
Given numbers has no common factors except 1. So, there LCM is their product i.e 49200
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/49200
Therefore, the GCF of Fractions 778/123,686/400 is 2/49200
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 123,400 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(123,400) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(123,400) x common factors =1 x 1 = 1
LCM(123,400) = ( 123 × 400 ) / 1
LCM(123,400) = 49200 / 1
LCM(123,400) = 49200
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 778,686?
The HCF of 778,686 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 778/123, 686/400?
Answer: GCF of Numerators as per given numbers 778/123, 686/400 is
GCF of Numerators i.e. for 778,686 is 2
LCM of denominators i.e. for 123,400 is 49200.
Thus, GCF of Fractions is 2/49200.Finally, GCF of Fractions for 778/123, 686/400 is 2/49200.