Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 88/31,22/14,30/16,38/12
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 88,22,30,38
Greatest Common Factor of Numerators i.e. GCF of 88,22,30,38 is 2 .
LCM of Denominators means LCM of 31,14,16,12 as per the given fractions.
LCM of 31,14,16,12 is 10416 as it is the smallest common factor for both these numbers.
Lets's calculate GCF of 88,22,30,38
2 | 88, 22, 30, 38 |
44, 11, 15, 19 |
∴ So the GCF of the given numbers is 2 = 2
Factors of 88
List of positive integer factors of 88 that divides 88 without a remainder.
1,2,4,8,11,22,44,88
Factors of 22
List of positive integer factors of 22 that divides 22 without a remainder.
1,2,11,22
Factors of 30
List of positive integer factors of 30 that divides 30 without a remainder.
1,2,3,5,6,10,15,30
Factors of 38
List of positive integer factors of 38 that divides 38 without a remainder.
1,2,19,38
Greatest Common Factor
We found the factors 88,22,30,38 . The biggest common factor number is the GCF number.
So the greatest common factor 88,22,30,38 is 2.
Lets's calculate LCM of 31,14,16,12
2 | 31, 14, 16, 12 |
2 | 31, 7, 8, 6 |
31, 7, 4, 3 |
∴ So the LCM of the given numbers is 2 x 2 x 31 x 7 x 4 x 3 = 10416
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/10416
Therefore, the GCF of Fractions 88/31,22/14,30/16,38/12 is 2/10416
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 31,14,16,12 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(31,14,16,12) = 1
common factors(in case of two or more numbers have common factors) = 8
GCF(31,14,16,12) x common factors =1 x 8 = 8
LCM(31,14,16,12) = ( 31 × 14 × 16 × 12 ) / 8
LCM(31,14,16,12) = 83328 / 8
LCM(31,14,16,12) = 10416
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 88/31, 22/14, 30/16, 38/12?
Answer: GCF of Numerators as per given numbers 88/31, 22/14, 30/16, 38/12 is
GCF of Numerators i.e. for 88,22,30,38 is 2
LCM of denominators i.e. for 31,14,16,12 is 10416.
Thus, GCF of Fractions is 2/10416.Finally, GCF of Fractions for 88/31, 22/14, 30/16, 38/12 is 2/10416.