Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 6/32,89/76,98/64,75/49
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 6,89,98,75
Greatest Common Factor of Numerators i.e. GCF of 6,89,98,75 is 1 .
LCM of Denominators means LCM of 32,76,64,49 as per the given fractions.
LCM of 32,76,64,49 is 59584 as it is the smallest common factor for both these numbers.
Lets's calculate GCF of 6,89,98,75
∴ So GCF of numbers is 1 because of no common factors present between them.
Factors of 6
List of positive integer factors of 6 that divides 6 without a remainder.
1,2,3,6
Factors of 89
List of positive integer factors of 89 that divides 89 without a remainder.
1,89
Factors of 98
List of positive integer factors of 98 that divides 98 without a remainder.
1,2,7,14,49,98
Factors of 75
List of positive integer factors of 75 that divides 75 without a remainder.
1,3,5,15,25,75
Greatest Common Factor
We found the factors 6,89,98,75 . The biggest common factor number is the GCF number.
So the greatest common factor 6,89,98,75 is 1.
Lets's calculate LCM of 32,76,64,49
2 | 32, 76, 64, 49 |
2 | 16, 38, 32, 49 |
2 | 8, 19, 16, 49 |
2 | 4, 19, 8, 49 |
2 | 2, 19, 4, 49 |
1, 19, 2, 49 |
∴ So the LCM of the given numbers is 2 x 2 x 2 x 2 x 2 x 1 x 19 x 2 x 49 = 59584
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/59584
Therefore, the GCF of Fractions 6/32,89/76,98/64,75/49 is 1/59584
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 32,76,64,49 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(32,76,64,49) = 1
common factors(in case of two or more numbers have common factors) = 128
GCF(32,76,64,49) x common factors =1 x 128 = 128
LCM(32,76,64,49) = ( 32 × 76 × 64 × 49 ) / 128
LCM(32,76,64,49) = 7626752 / 128
LCM(32,76,64,49) = 59584
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 6/32, 89/76, 98/64, 75/49?
Answer: GCF of Numerators as per given numbers 6/32, 89/76, 98/64, 75/49 is
GCF of Numerators i.e. for 6,89,98,75 is 1
LCM of denominators i.e. for 32,76,64,49 is 59584.
Thus, GCF of Fractions is 1/59584.Finally, GCF of Fractions for 6/32, 89/76, 98/64, 75/49 is 1/59584.