Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 10/66,88/27,12/40,274/20
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 10,88,12,274
Greatest Common Factor of Numerators i.e. GCF of 10,88,12,274 is 2 .
LCM of Denominators means LCM of 66,27,40,20 as per the given fractions.
LCM of 66,27,40,20 is 11880 as it is the smallest common factor for both these numbers.
Lets's calculate GCF of 10,88,12,274
2 | 10, 88, 12, 274 |
5, 44, 6, 137 |
∴ So the GCF of the given numbers is 2 = 2
Factors of 10
List of positive integer factors of 10 that divides 10 without a remainder.
1,2,5,10
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 12
List of positive integer factors of 12 that divides 12 without a remainder.
1,2,3,4,6,12
Factors of 274
List of positive integer factors of 274 that divides 274 without a remainder.
1,2,137,274
Greatest Common Factor
We found the factors 10,88,12,274 . The biggest common factor number is the GCF number.
So the greatest common factor 10,88,12,274 is 2.
Lets's calculate LCM of 66,27,40,20
2 | 66, 27, 40, 20 |
2 | 33, 27, 20, 10 |
3 | 33, 27, 5, 10 |
5 | 11, 9, 5, 10 |
11, 9, 1, 2 |
∴ So the LCM of the given numbers is 2 x 2 x 3 x 5 x 11 x 9 x 1 x 2 = 11880
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/11880
Therefore, the GCF of Fractions 10/66,88/27,12/40,274/20 is 2/11880
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 66,27,40,20 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(66,27,40,20) = 1
common factors(in case of two or more numbers have common factors) = 120
GCF(66,27,40,20) x common factors =1 x 120 = 120
LCM(66,27,40,20) = ( 66 × 27 × 40 × 20 ) / 120
LCM(66,27,40,20) = 1425600 / 120
LCM(66,27,40,20) = 11880
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 10/66, 88/27, 12/40, 274/20?
Answer: GCF of Numerators as per given numbers 10/66, 88/27, 12/40, 274/20 is
GCF of Numerators i.e. for 10,88,12,274 is 2
LCM of denominators i.e. for 66,27,40,20 is 11880.
Thus, GCF of Fractions is 2/11880.Finally, GCF of Fractions for 10/66, 88/27, 12/40, 274/20 is 2/11880.