Use our free GCF of Fractions Calculator tool to compute the GCF of 780/354, 418/664 i.e 2/117528 easily. The following is the detailed procedure to determine the greatest common factor of fractions 780/354, 418/664.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 780/354,418/664
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 780/354,418/664, numerators are 780,418
Denominators are 354,664
The GCF of 780,418 is 2 .
LCM of 354,664 is 117528.
The greatest common factor of 780/354,418/664 = [GCF of 780,418]/[LCM of 354,664]= 2/117528
Therefore, the GCF of 780/354,418/664 is 2/117528.
To find the highest common factor of 780,418, 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 418 are 1, 2, 11, 19, 22, 38, 209, 418
The HCF of 780,418 is 2.
Lets's calculate GCF of 780,418
2 | 780, 418 |
390, 209 |
∴ So the GCF of the given numbers is 2 = 2
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 418
:1,2,11,19,22,38,209,418
Greatest Common Factor
We found the factors 780,418 . The biggest common factor number is the GCF number.
So the greatest common factor 780,418 is 2.
Lets's calculate LCM of 354,664
2 | 354, 664 |
177, 332 |
∴ So the LCM of the given numbers is 2 x 177 x 332 = 117528
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/117528
Therefore, the GCF of Fractions 780/354,418/664 is 2/117528
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 354,664 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(354,664) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(354,664) x common factors =2 x 1 = 2
LCM(354,664) = ( 354 × 664 ) / 2
LCM(354,664) = 235056 / 2
LCM(354,664) = 117528
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 780,418?
The HCF of 780,418 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 780/354, 418/664?
Answer: GCF of Numerators as per given numbers 780/354, 418/664 is
GCF of Numerators i.e. for 780,418 is 2
LCM of denominators i.e. for 354,664 is 117528.
Thus, GCF of Fractions is 2/117528.Finally, GCF of Fractions for 780/354, 418/664 is 2/117528.