Use our free GCF of Fractions Calculator tool to compute the GCF of 780/670, 710/820 i.e 10/54940 easily. The following is the detailed procedure to determine the greatest common factor of fractions 780/670, 710/820.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 780/670,710/820
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 780/670,710/820, numerators are 780,710
Denominators are 670,820
The GCF of 780,710 is 10 .
LCM of 670,820 is 54940.
The greatest common factor of 780/670,710/820 = [GCF of 780,710]/[LCM of 670,820]= 10/54940
Therefore, the GCF of 780/670,710/820 is 10/54940.
To find the highest common factor of 780,710, we have to find the factors of both numbers and list the highest common factor.
The factors of 780 are 1, 2, 3, 4, 5, 6, 10, 12, 13, 15, 20, 26, 30, 39, 52, 60, 65, 78, 130, 156, 195, 260, 390, 780
The factors of 710 are 1, 2, 5, 10, 71, 142, 355, 710
The HCF of 780,710 is 10.
Lets's calculate GCF of 780,710
2 | 780, 710 |
5 | 390, 355 |
78, 71 |
∴ So the GCF of the given numbers is 2 x 5 = 10
Now, list down the factors of 780
:1,2,3,4,5,6,10,12,13,15,20,26,30,39,52,60,65,78,130,156,195,260,390,780
Now, list down the factors of 710
:1,2,5,10,71,142,355,710
Greatest Common Factor
We found the factors 780,710 . The biggest common factor number is the GCF number.
So the greatest common factor 780,710 is 10.
Lets's calculate LCM of 670,820
2 | 670, 820 |
5 | 335, 410 |
67, 82 |
∴ So the LCM of the given numbers is 2 x 5 x 67 x 82 = 54940
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 10/54940
Therefore, the GCF of Fractions 780/670,710/820 is 10/54940
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 670,820 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(670,820) = 10
common factors(in case of two or more numbers have common factors) = 1
GCF(670,820) x common factors =10 x 1 = 10
LCM(670,820) = ( 670 × 820 ) / 10
LCM(670,820) = 549400 / 10
LCM(670,820) = 54940
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 780,710?
The HCF of 780,710 is 10
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 780/670, 710/820?
Answer: GCF of Numerators as per given numbers 780/670, 710/820 is
GCF of Numerators i.e. for 780,710 is 10
LCM of denominators i.e. for 670,820 is 54940.
Thus, GCF of Fractions is 10/54940.Finally, GCF of Fractions for 780/670, 710/820 is 10/54940.