Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 82/87,40/76,92/66,61/40
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 82,40,92,61
Greatest Common Factor of Numerators i.e. GCF of 82,40,92,61 is 1 .
LCM of Denominators means LCM of 87,76,66,40 as per the given fractions.
LCM of 87,76,66,40 is 727320 as it is the smallest common factor for both these numbers.
Lets's calculate GCF of 82,40,92,61
∴ So GCF of numbers is 1 because of no common factors present between them.
Factors of 82
List of positive integer factors of 82 that divides 82 without a remainder.
1,2,41,82
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 92
List of positive integer factors of 92 that divides 92 without a remainder.
1,2,4,23,46,92
Factors of 61
List of positive integer factors of 61 that divides 61 without a remainder.
1,61
Greatest Common Factor
We found the factors 82,40,92,61 . The biggest common factor number is the GCF number.
So the greatest common factor 82,40,92,61 is 1.
Lets's calculate LCM of 87,76,66,40
2 | 87, 76, 66, 40 |
2 | 87, 38, 33, 20 |
3 | 87, 19, 33, 10 |
29, 19, 11, 10 |
∴ So the LCM of the given numbers is 2 x 2 x 3 x 29 x 19 x 11 x 10 = 727320
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/727320
Therefore, the GCF of Fractions 82/87,40/76,92/66,61/40 is 1/727320
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 87,76,66,40 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(87,76,66,40) = 1
common factors(in case of two or more numbers have common factors) = 24
GCF(87,76,66,40) x common factors =1 x 24 = 24
LCM(87,76,66,40) = ( 87 × 76 × 66 × 40 ) / 24
LCM(87,76,66,40) = 17455680 / 24
LCM(87,76,66,40) = 727320
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 82/87, 40/76, 92/66, 61/40?
Answer: GCF of Numerators as per given numbers 82/87, 40/76, 92/66, 61/40 is
GCF of Numerators i.e. for 82,40,92,61 is 1
LCM of denominators i.e. for 87,76,66,40 is 727320.
Thus, GCF of Fractions is 1/727320.Finally, GCF of Fractions for 82/87, 40/76, 92/66, 61/40 is 1/727320.