Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 31/19,49/24,686/51
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 31,49,686
Greatest Common Factor of Numerators i.e. GCF of 31,49,686 is 1 .
LCM of Denominators means LCM of 19,24,51 as per the given fractions.
LCM of 19,24,51 is 7752 as it is the smallest common factor for both these numbers.
Lets's calculate GCF of 31,49,686
∴ So GCF of numbers is 1 because of no common factors present between them.
Factors of 31
List of positive integer factors of 31 that divides 31 without a remainder.
1,31
Factors of 49
List of positive integer factors of 49 that divides 49 without a remainder.
1,7,49
Factors of 686
List of positive integer factors of 686 that divides 686 without a remainder.
1,2,7,14,49,98,343,686
Greatest Common Factor
We found the factors 31,49,686 . The biggest common factor number is the GCF number.
So the greatest common factor 31,49,686 is 1.
Lets's calculate LCM of 19,24,51
3 | 19, 24, 51 |
19, 8, 17 |
∴ So the LCM of the given numbers is 3 x 19 x 8 x 17 = 7752
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/7752
Therefore, the GCF of Fractions 31/19,49/24,686/51 is 1/7752
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 19,24,51 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(19,24,51) = 1
common factors(in case of two or more numbers have common factors) = 3
GCF(19,24,51) x common factors =1 x 3 = 3
LCM(19,24,51) = ( 19 × 24 × 51 ) / 3
LCM(19,24,51) = 23256 / 3
LCM(19,24,51) = 7752
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 31/19, 49/24, 686/51?
Answer: GCF of Numerators as per given numbers 31/19, 49/24, 686/51 is
GCF of Numerators i.e. for 31,49,686 is 1
LCM of denominators i.e. for 19,24,51 is 7752.
Thus, GCF of Fractions is 1/7752.Finally, GCF of Fractions for 31/19, 49/24, 686/51 is 1/7752.