Use our free GCF of Fractions Calculator tool to compute the GCF of 780/242, 702/770 i.e 78/8470 easily. The following is the detailed procedure to determine the greatest common factor of fractions 780/242, 702/770.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 780/242,702/770
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 780/242,702/770, numerators are 780,702
Denominators are 242,770
The GCF of 780,702 is 78 .
LCM of 242,770 is 8470.
The greatest common factor of 780/242,702/770 = [GCF of 780,702]/[LCM of 242,770]= 78/8470
Therefore, the GCF of 780/242,702/770 is 78/8470.
To find the highest common factor of 780,702, 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 702 are 1, 2, 3, 6, 9, 13, 18, 26, 27, 39, 54, 78, 117, 234, 351, 702
The HCF of 780,702 is 78.
Lets's calculate GCF of 780,702
2 | 780, 702 |
3 | 390, 351 |
13 | 130, 117 |
10, 9 |
∴ So the GCF of the given numbers is 2 x 3 x 13 = 78
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 702
:1,2,3,6,9,13,18,26,27,39,54,78,117,234,351,702
Greatest Common Factor
We found the factors 780,702 . The biggest common factor number is the GCF number.
So the greatest common factor 780,702 is 78.
Lets's calculate LCM of 242,770
2 | 242, 770 |
11 | 121, 385 |
11, 35 |
∴ So the LCM of the given numbers is 2 x 11 x 11 x 35 = 8470
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 78/8470
Therefore, the GCF of Fractions 780/242,702/770 is 78/8470
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 242,770 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(242,770) = 22
common factors(in case of two or more numbers have common factors) = 1
GCF(242,770) x common factors =22 x 1 = 22
LCM(242,770) = ( 242 × 770 ) / 22
LCM(242,770) = 186340 / 22
LCM(242,770) = 8470
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 780,702?
The HCF of 780,702 is 78
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 780/242, 702/770?
Answer: GCF of Numerators as per given numbers 780/242, 702/770 is
GCF of Numerators i.e. for 780,702 is 78
LCM of denominators i.e. for 242,770 is 8470.
Thus, GCF of Fractions is 78/8470.Finally, GCF of Fractions for 780/242, 702/770 is 78/8470.