Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 70/20,84/84,74/55,20/57
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 70,84,74,20
Greatest Common Factor of Numerators i.e. GCF of 70,84,74,20 is 2 .
LCM of Denominators means LCM of 20,84,55,57 as per the given fractions.
LCM of 20,84,55,57 is 87780 as it is the smallest common factor for both these numbers.
Lets's calculate GCF of 70,84,74,20
2 | 70, 84, 74, 20 |
35, 42, 37, 10 |
∴ So the GCF of the given numbers is 2 = 2
Factors of 70
List of positive integer factors of 70 that divides 70 without a remainder.
1,2,5,7,10,14,35,70
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 74
List of positive integer factors of 74 that divides 74 without a remainder.
1,2,37,74
Factors of 20
List of positive integer factors of 20 that divides 20 without a remainder.
1,2,4,5,10,20
Greatest Common Factor
We found the factors 70,84,74,20 . The biggest common factor number is the GCF number.
So the greatest common factor 70,84,74,20 is 2.
Lets's calculate LCM of 20,84,55,57
2 | 20, 84, 55, 57 |
2 | 10, 42, 55, 57 |
3 | 5, 21, 55, 57 |
5 | 5, 7, 55, 19 |
1, 7, 11, 19 |
∴ So the LCM of the given numbers is 2 x 2 x 3 x 5 x 1 x 7 x 11 x 19 = 87780
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/87780
Therefore, the GCF of Fractions 70/20,84/84,74/55,20/57 is 2/87780
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 20,84,55,57 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(20,84,55,57) = 1
common factors(in case of two or more numbers have common factors) = 60
GCF(20,84,55,57) x common factors =1 x 60 = 60
LCM(20,84,55,57) = ( 20 × 84 × 55 × 57 ) / 60
LCM(20,84,55,57) = 5266800 / 60
LCM(20,84,55,57) = 87780
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 70/20, 84/84, 74/55, 20/57?
Answer: GCF of Numerators as per given numbers 70/20, 84/84, 74/55, 20/57 is
GCF of Numerators i.e. for 70,84,74,20 is 2
LCM of denominators i.e. for 20,84,55,57 is 87780.
Thus, GCF of Fractions is 2/87780.Finally, GCF of Fractions for 70/20, 84/84, 74/55, 20/57 is 2/87780.