Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 78/84,24/88,768/812
Formula to find GCF of Fractions is
GCF = GCF of Numerators/LCM of Denominators
As per the formula GCF of Fractions let’s split into two parts and find the GCF of Numerators and LCM of Denominators
In the given fractions GCF of Numerators means GCF of 78,24,768
Greatest Common Factor of Numerators i.e. GCF of 78,24,768 is 6 .
LCM of Denominators means LCM of 84,88,812 as per the given fractions.
LCM of 84,88,812 is 53592 as it is the smallest common factor for both these numbers.
Lets's calculate GCF of 78,24,768
2 | 78, 24, 768 |
3 | 39, 12, 384 |
13, 4, 128 |
∴ So the GCF of the given numbers is 2 x 3 = 6
Factors of 78
List of positive integer factors of 78 that divides 78 without a remainder.
1,2,3,6,13,26,39,78
Factors of 24
List of positive integer factors of 24 that divides 24 without a remainder.
1,2,3,4,6,8,12,24
Factors of 768
List of positive integer factors of 768 that divides 768 without a remainder.
1,2,3,4,6,8,12,16,24,32,48,64,96,128,192,256,384,768
Greatest Common Factor
We found the factors 78,24,768 . The biggest common factor number is the GCF number.
So the greatest common factor 78,24,768 is 6.
Lets's calculate LCM of 84,88,812
2 | 84, 88, 812 |
2 | 42, 44, 406 |
7 | 21, 22, 203 |
3, 22, 29 |
∴ So the LCM of the given numbers is 2 x 2 x 7 x 3 x 22 x 29 = 53592
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 6/53592
Therefore, the GCF of Fractions 78/84,24/88,768/812 is 6/53592
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 84,88,812 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(84,88,812) = 4
common factors(in case of two or more numbers have common factors) = 28
GCF(84,88,812) x common factors =4 x 28 = 112
LCM(84,88,812) = ( 84 × 88 × 812 ) / 112
LCM(84,88,812) = 6002304 / 112
LCM(84,88,812) = 53592
Here are some samples of GCF of Fractions calculations.
Here are some samples of GCF of Fractions calculations.
1. 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.
2. What is the GCF of Fractions for 78/84, 24/88, 768/812?
Answer: GCF of Numerators as per given numbers 78/84, 24/88, 768/812 is
GCF of Numerators i.e. for 78,24,768 is 6
LCM of denominators i.e. for 84,88,812 is 53592.
Thus, GCF of Fractions is 6/53592.Finally, GCF of Fractions for 78/84, 24/88, 768/812 is 6/53592.