Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 12/78,76/23,42/23,284/78
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 12,76,42,284
Greatest Common Factor of Numerators i.e. GCF of 12,76,42,284 is 2 .
LCM of Denominators means LCM of 78,23,23,78 as per the given fractions.
LCM of 78,23,23,78 is 1794 as it is the smallest common factor for both these numbers.
Lets's calculate GCF of 12,76,42,284
2 | 12, 76, 42, 284 |
6, 38, 21, 142 |
∴ So the GCF of the given numbers is 2 = 2
Factors of 12
List of positive integer factors of 12 that divides 12 without a remainder.
1,2,3,4,6,12
Factors of 76
List of positive integer factors of 76 that divides 76 without a remainder.
1,2,4,19,38,76
Factors of 42
List of positive integer factors of 42 that divides 42 without a remainder.
1,2,3,6,7,14,21,42
Factors of 284
List of positive integer factors of 284 that divides 284 without a remainder.
1,2,4,71,142,284
Greatest Common Factor
We found the factors 12,76,42,284 . The biggest common factor number is the GCF number.
So the greatest common factor 12,76,42,284 is 2.
Lets's calculate LCM of 78,23,23,78
2 | 78, 23, 23, 78 |
3 | 39, 23, 23, 39 |
13 | 13, 23, 23, 13 |
23 | 1, 23, 23, 1 |
1, 1, 1, 1 |
∴ So the LCM of the given numbers is 2 x 3 x 13 x 23 x 1 x 1 x 1 x 1 = 1794
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/1794
Therefore, the GCF of Fractions 12/78,76/23,42/23,284/78 is 2/1794
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 78,23,23,78 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(78,23,23,78) = 1
common factors(in case of two or more numbers have common factors) = 1794
GCF(78,23,23,78) x common factors =1 x 1794 = 1794
LCM(78,23,23,78) = ( 78 × 23 × 23 × 78 ) / 1794
LCM(78,23,23,78) = 3218436 / 1794
LCM(78,23,23,78) = 1794
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 12/78, 76/23, 42/23, 284/78?
Answer: GCF of Numerators as per given numbers 12/78, 76/23, 42/23, 284/78 is
GCF of Numerators i.e. for 12,76,42,284 is 2
LCM of denominators i.e. for 78,23,23,78 is 1794.
Thus, GCF of Fractions is 2/1794.Finally, GCF of Fractions for 12/78, 76/23, 42/23, 284/78 is 2/1794.