Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 61/80,40/53,59/96,56/71
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 61,40,59,56
Greatest Common Factor of Numerators i.e. GCF of 61,40,59,56 is 1 .
LCM of Denominators means LCM of 80,53,96,71 as per the given fractions.
LCM of 80,53,96,71 is 1806240 as it is the smallest common factor for both these numbers.
Lets's calculate GCF of 61,40,59,56
∴ So GCF of numbers is 1 because of no common factors present between them.
Factors of 61
List of positive integer factors of 61 that divides 61 without a remainder.
1,61
Factors of 40
List of positive integer factors of 40 that divides 40 without a remainder.
1,2,4,5,8,10,20,40
Factors of 59
List of positive integer factors of 59 that divides 59 without a remainder.
1,59
Factors of 56
List of positive integer factors of 56 that divides 56 without a remainder.
1,2,4,7,8,14,28,56
Greatest Common Factor
We found the factors 61,40,59,56 . The biggest common factor number is the GCF number.
So the greatest common factor 61,40,59,56 is 1.
Lets's calculate LCM of 80,53,96,71
2 | 80, 53, 96, 71 |
2 | 40, 53, 48, 71 |
2 | 20, 53, 24, 71 |
2 | 10, 53, 12, 71 |
5, 53, 6, 71 |
∴ So the LCM of the given numbers is 2 x 2 x 2 x 2 x 5 x 53 x 6 x 71 = 1806240
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/1806240
Therefore, the GCF of Fractions 61/80,40/53,59/96,56/71 is 1/1806240
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 80,53,96,71 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(80,53,96,71) = 1
common factors(in case of two or more numbers have common factors) = 16
GCF(80,53,96,71) x common factors =1 x 16 = 16
LCM(80,53,96,71) = ( 80 × 53 × 96 × 71 ) / 16
LCM(80,53,96,71) = 28899840 / 16
LCM(80,53,96,71) = 1806240
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 61/80, 40/53, 59/96, 56/71?
Answer: GCF of Numerators as per given numbers 61/80, 40/53, 59/96, 56/71 is
GCF of Numerators i.e. for 61,40,59,56 is 1
LCM of denominators i.e. for 80,53,96,71 is 1806240.
Thus, GCF of Fractions is 1/1806240.Finally, GCF of Fractions for 61/80, 40/53, 59/96, 56/71 is 1/1806240.