Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 84/32,11/80,60/70,14/49
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 84,11,60,14
Greatest Common Factor of Numerators i.e. GCF of 84,11,60,14 is 1 .
LCM of Denominators means LCM of 32,80,70,49 as per the given fractions.
LCM of 32,80,70,49 is 7840 as it is the smallest common factor for both these numbers.
Lets's calculate GCF of 84,11,60,14
∴ So GCF of numbers is 1 because of no common factors present between them.
Factors of 84
List of positive integer factors of 84 that divides 84 without a remainder.
1,2,3,4,6,7,12,14,21,28,42,84
Factors of 11
List of positive integer factors of 11 that divides 11 without a remainder.
1,11
Factors of 60
List of positive integer factors of 60 that divides 60 without a remainder.
1,2,3,4,5,6,10,12,15,20,30,60
Factors of 14
List of positive integer factors of 14 that divides 14 without a remainder.
1,2,7,14
Greatest Common Factor
We found the factors 84,11,60,14 . The biggest common factor number is the GCF number.
So the greatest common factor 84,11,60,14 is 1.
Lets's calculate LCM of 32,80,70,49
2 | 32, 80, 70, 49 |
2 | 16, 40, 35, 49 |
2 | 8, 20, 35, 49 |
2 | 4, 10, 35, 49 |
5 | 2, 5, 35, 49 |
7 | 2, 1, 7, 49 |
2, 1, 1, 7 |
∴ So the LCM of the given numbers is 2 x 2 x 2 x 2 x 5 x 7 x 2 x 1 x 1 x 7 = 7840
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/7840
Therefore, the GCF of Fractions 84/32,11/80,60/70,14/49 is 1/7840
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 32,80,70,49 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(32,80,70,49) = 1
common factors(in case of two or more numbers have common factors) = 1120
GCF(32,80,70,49) x common factors =1 x 1120 = 1120
LCM(32,80,70,49) = ( 32 × 80 × 70 × 49 ) / 1120
LCM(32,80,70,49) = 8780800 / 1120
LCM(32,80,70,49) = 7840
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 84/32, 11/80, 60/70, 14/49?
Answer: GCF of Numerators as per given numbers 84/32, 11/80, 60/70, 14/49 is
GCF of Numerators i.e. for 84,11,60,14 is 1
LCM of denominators i.e. for 32,80,70,49 is 7840.
Thus, GCF of Fractions is 1/7840.Finally, GCF of Fractions for 84/32, 11/80, 60/70, 14/49 is 1/7840.