Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 48/64,98/49,55/20,91/32
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 48,98,55,91
Greatest Common Factor of Numerators i.e. GCF of 48,98,55,91 is 1 .
LCM of Denominators means LCM of 64,49,20,32 as per the given fractions.
LCM of 64,49,20,32 is 15680 as it is the smallest common factor for both these numbers.
Lets's calculate GCF of 48,98,55,91
∴ So GCF of numbers is 1 because of no common factors present between them.
Factors of 48
List of positive integer factors of 48 that divides 48 without a remainder.
1,2,3,4,6,8,12,16,24,48
Factors of 98
List of positive integer factors of 98 that divides 98 without a remainder.
1,2,7,14,49,98
Factors of 55
List of positive integer factors of 55 that divides 55 without a remainder.
1,5,11,55
Factors of 91
List of positive integer factors of 91 that divides 91 without a remainder.
1,7,13,91
Greatest Common Factor
We found the factors 48,98,55,91 . The biggest common factor number is the GCF number.
So the greatest common factor 48,98,55,91 is 1.
Lets's calculate LCM of 64,49,20,32
2 | 64, 49, 20, 32 |
2 | 32, 49, 10, 16 |
2 | 8, 49, 5, 16 |
2 | 4, 49, 5, 8 |
2 | 2, 49, 5, 4 |
1, 49, 5, 2 |
∴ So the LCM of the given numbers is 2 x 2 x 2 x 2 x 2 x 1 x 49 x 5 x 2 = 15680
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/15680
Therefore, the GCF of Fractions 48/64,98/49,55/20,91/32 is 1/15680
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 64,49,20,32 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(64,49,20,32) = 1
common factors(in case of two or more numbers have common factors) = 128
GCF(64,49,20,32) x common factors =1 x 128 = 128
LCM(64,49,20,32) = ( 64 × 49 × 20 × 32 ) / 128
LCM(64,49,20,32) = 2007040 / 128
LCM(64,49,20,32) = 15680
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 48/64, 98/49, 55/20, 91/32?
Answer: GCF of Numerators as per given numbers 48/64, 98/49, 55/20, 91/32 is
GCF of Numerators i.e. for 48,98,55,91 is 1
LCM of denominators i.e. for 64,49,20,32 is 15680.
Thus, GCF of Fractions is 1/15680.Finally, GCF of Fractions for 48/64, 98/49, 55/20, 91/32 is 1/15680.