Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 42/78,94/65,39/98,50/36
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 42,94,39,50
Greatest Common Factor of Numerators i.e. GCF of 42,94,39,50 is 1 .
LCM of Denominators means LCM of 78,65,98,36 as per the given fractions.
LCM of 78,65,98,36 is 114660 as it is the smallest common factor for both these numbers.
Lets's calculate GCF of 42,94,39,50
∴ So GCF of numbers is 1 because of no common factors present between them.
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 94
List of positive integer factors of 94 that divides 94 without a remainder.
1,2,47,94
Factors of 39
List of positive integer factors of 39 that divides 39 without a remainder.
1,3,13,39
Factors of 50
List of positive integer factors of 50 that divides 50 without a remainder.
1,2,5,10,25,50
Greatest Common Factor
We found the factors 42,94,39,50 . The biggest common factor number is the GCF number.
So the greatest common factor 42,94,39,50 is 1.
Lets's calculate LCM of 78,65,98,36
2 | 78, 65, 98, 36 |
3 | 39, 65, 49, 18 |
13 | 13, 65, 49, 6 |
1, 5, 49, 6 |
∴ So the LCM of the given numbers is 2 x 3 x 13 x 1 x 5 x 49 x 6 = 114660
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/114660
Therefore, the GCF of Fractions 42/78,94/65,39/98,50/36 is 1/114660
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 78,65,98,36 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(78,65,98,36) = 1
common factors(in case of two or more numbers have common factors) = 156
GCF(78,65,98,36) x common factors =1 x 156 = 156
LCM(78,65,98,36) = ( 78 × 65 × 98 × 36 ) / 156
LCM(78,65,98,36) = 17886960 / 156
LCM(78,65,98,36) = 114660
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 42/78, 94/65, 39/98, 50/36?
Answer: GCF of Numerators as per given numbers 42/78, 94/65, 39/98, 50/36 is
GCF of Numerators i.e. for 42,94,39,50 is 1
LCM of denominators i.e. for 78,65,98,36 is 114660.
Thus, GCF of Fractions is 1/114660.Finally, GCF of Fractions for 42/78, 94/65, 39/98, 50/36 is 1/114660.