Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 2/89,42/54,45/65,31/98
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 2,42,45,31
Greatest Common Factor of Numerators i.e. GCF of 2,42,45,31 is 1 .
LCM of Denominators means LCM of 89,54,65,98 as per the given fractions.
LCM of 89,54,65,98 is 15307110 as it is the smallest common factor for both these numbers.
Lets's calculate GCF of 2,42,45,31
∴ So GCF of numbers is 1 because of no common factors present between them.
Factors of 2
List of positive integer factors of 2 that divides 2 without a remainder.
1,2
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 45
List of positive integer factors of 45 that divides 45 without a remainder.
1,3,5,9,15,45
Factors of 31
List of positive integer factors of 31 that divides 31 without a remainder.
1,31
Greatest Common Factor
We found the factors 2,42,45,31 . The biggest common factor number is the GCF number.
So the greatest common factor 2,42,45,31 is 1.
Lets's calculate LCM of 89,54,65,98
2 | 89, 54, 65, 98 |
89, 27, 65, 49 |
∴ So the LCM of the given numbers is 2 x 89 x 27 x 65 x 49 = 15307110
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/15307110
Therefore, the GCF of Fractions 2/89,42/54,45/65,31/98 is 1/15307110
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 89,54,65,98 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(89,54,65,98) = 1
common factors(in case of two or more numbers have common factors) = 2
GCF(89,54,65,98) x common factors =1 x 2 = 2
LCM(89,54,65,98) = ( 89 × 54 × 65 × 98 ) / 2
LCM(89,54,65,98) = 30614220 / 2
LCM(89,54,65,98) = 15307110
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 2/89, 42/54, 45/65, 31/98?
Answer: GCF of Numerators as per given numbers 2/89, 42/54, 45/65, 31/98 is
GCF of Numerators i.e. for 2,42,45,31 is 1
LCM of denominators i.e. for 89,54,65,98 is 15307110.
Thus, GCF of Fractions is 1/15307110.Finally, GCF of Fractions for 2/89, 42/54, 45/65, 31/98 is 1/15307110.