Use our free GCF of Fractions Calculator tool to compute the GCF of 760/774, 975/677 i.e 5/523998 easily. The following is the detailed procedure to determine the greatest common factor of fractions 760/774, 975/677.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 760/774,975/677
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 760/774,975/677, numerators are 760,975
Denominators are 774,677
The GCF of 760,975 is 5 .
LCM of 774,677 is 523998.
The greatest common factor of 760/774,975/677 = [GCF of 760,975]/[LCM of 774,677]= 5/523998
Therefore, the GCF of 760/774,975/677 is 5/523998.
To find the highest common factor of 760,975, we have to find the factors of both numbers and list the highest common factor.
The factors of 760 are 1, 2, 4, 5, 8, 10, 19, 20, 38, 40, 76, 95, 152, 190, 380, 760
The factors of 975 are 1, 3, 5, 13, 15, 25, 39, 65, 75, 195, 325, 975
The HCF of 760,975 is 5.
Lets's calculate GCF of 760,975
5 | 760, 975 |
152, 195 |
∴ So the GCF of the given numbers is 5 = 5
Now, list down the factors of 760
:1,2,4,5,8,10,19,20,38,40,76,95,152,190,380,760
Now, list down the factors of 975
:1,3,5,13,15,25,39,65,75,195,325,975
Greatest Common Factor
We found the factors 760,975 . The biggest common factor number is the GCF number.
So the greatest common factor 760,975 is 5.
Lets's calculate LCM of 774,677
Given numbers has no common factors except 1. So, there LCM is their product i.e 523998
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 5/523998
Therefore, the GCF of Fractions 760/774,975/677 is 5/523998
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 774,677 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(774,677) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(774,677) x common factors =1 x 1 = 1
LCM(774,677) = ( 774 × 677 ) / 1
LCM(774,677) = 523998 / 1
LCM(774,677) = 523998
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 760,975?
The HCF of 760,975 is 5
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 760/774, 975/677?
Answer: GCF of Numerators as per given numbers 760/774, 975/677 is
GCF of Numerators i.e. for 760,975 is 5
LCM of denominators i.e. for 774,677 is 523998.
Thus, GCF of Fractions is 5/523998.Finally, GCF of Fractions for 760/774, 975/677 is 5/523998.