Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 28/66,52/64,61/70,317/56
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 28,52,61,317
Greatest Common Factor of Numerators i.e. GCF of 28,52,61,317 is 1 .
LCM of Denominators means LCM of 66,64,70,56 as per the given fractions.
LCM of 66,64,70,56 is 73920 as it is the smallest common factor for both these numbers.
Lets's calculate GCF of 28,52,61,317
∴ So GCF of numbers is 1 because of no common factors present between them.
Factors of 28
List of positive integer factors of 28 that divides 28 without a remainder.
1,2,4,7,14,28
Factors of 52
List of positive integer factors of 52 that divides 52 without a remainder.
1,2,4,13,26,52
Factors of 61
List of positive integer factors of 61 that divides 61 without a remainder.
1,61
Factors of 317
List of positive integer factors of 317 that divides 317 without a remainder.
1,317
Greatest Common Factor
We found the factors 28,52,61,317 . The biggest common factor number is the GCF number.
So the greatest common factor 28,52,61,317 is 1.
Lets's calculate LCM of 66,64,70,56
2 | 66, 64, 70, 56 |
2 | 33, 32, 35, 28 |
2 | 33, 16, 35, 14 |
7 | 33, 8, 35, 7 |
33, 8, 5, 1 |
∴ So the LCM of the given numbers is 2 x 2 x 2 x 7 x 33 x 8 x 5 x 1 = 73920
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/73920
Therefore, the GCF of Fractions 28/66,52/64,61/70,317/56 is 1/73920
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 66,64,70,56 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(66,64,70,56) = 2
common factors(in case of two or more numbers have common factors) = 112
GCF(66,64,70,56) x common factors =2 x 112 = 224
LCM(66,64,70,56) = ( 66 × 64 × 70 × 56 ) / 224
LCM(66,64,70,56) = 16558080 / 224
LCM(66,64,70,56) = 73920
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 28/66, 52/64, 61/70, 317/56?
Answer: GCF of Numerators as per given numbers 28/66, 52/64, 61/70, 317/56 is
GCF of Numerators i.e. for 28,52,61,317 is 1
LCM of denominators i.e. for 66,64,70,56 is 73920.
Thus, GCF of Fractions is 1/73920.Finally, GCF of Fractions for 28/66, 52/64, 61/70, 317/56 is 1/73920.