Use our free GCF of Fractions Calculator tool to compute the GCF of 78/66, 92/109, 260/312 i.e 2/374088 easily. The following is the detailed procedure to determine the greatest common factor of fractions 78/66, 92/109, 260/312.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 78/66,92/109,260/312
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 78/66,92/109,260/312, numerators are 78,92,260
Denominators are 66,109,312
The GCF of 78,92,260 is 2 .
LCM of 66,109,312 is 374088.
The greatest common factor of 78/66,92/109,260/312 = [GCF of 78,92,260]/[LCM of 66,109,312]= 2/374088
Therefore, the GCF of 78/66,92/109,260/312 is 2/374088.
To find the highest common factor of 78,92,260, we have to find the factors of both numbers and list the highest common factor.
The factors of 78 are 1, 2, 3, 6, 13, 26, 39, 78
The factors of 92 are 1, 2, 4, 23, 46, 92
The factors of 260 are 1, 2, 4, 5, 10, 13, 20, 26, 52, 65, 130, 260
The HCF of 78,92,260 is 2.
Lets's calculate GCF of 78,92,260
2 | 78, 92, 260 |
39, 46, 130 |
∴ So the GCF of the given numbers is 2 = 2
Now, list down the factors of 78
:1,2,3,6,13,26,39,78
Now, list down the factors of 92
:1,2,4,23,46,92
Now, list down the factors of 260
:1,2,4,5,10,13,20,26,52,65,130,260
Greatest Common Factor
We found the factors 78,92,260 . The biggest common factor number is the GCF number.
So the greatest common factor 78,92,260 is 2.
Lets's calculate LCM of 66,109,312
2 | 66, 109, 312 |
3 | 33, 109, 156 |
11, 109, 52 |
∴ So the LCM of the given numbers is 2 x 3 x 11 x 109 x 52 = 374088
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/374088
Therefore, the GCF of Fractions 78/66,92/109,260/312 is 2/374088
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 66,109,312 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(66,109,312) = 1
common factors(in case of two or more numbers have common factors) = 6
GCF(66,109,312) x common factors =1 x 6 = 6
LCM(66,109,312) = ( 66 × 109 × 312 ) / 6
LCM(66,109,312) = 2244528 / 6
LCM(66,109,312) = 374088
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 78,92,260?
The HCF of 78,92,260 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 78/66, 92/109, 260/312?
Answer: GCF of Numerators as per given numbers 78/66, 92/109, 260/312 is
GCF of Numerators i.e. for 78,92,260 is 2
LCM of denominators i.e. for 66,109,312 is 374088.
Thus, GCF of Fractions is 2/374088.Finally, GCF of Fractions for 78/66, 92/109, 260/312 is 2/374088.