Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 68/74,49/74,84/95,40/28
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 68,49,84,40
Greatest Common Factor of Numerators i.e. GCF of 68,49,84,40 is 1 .
LCM of Denominators means LCM of 74,74,95,28 as per the given fractions.
LCM of 74,74,95,28 is 98420 as it is the smallest common factor for both these numbers.
Lets's calculate GCF of 68,49,84,40
∴ So GCF of numbers is 1 because of no common factors present between them.
Factors of 68
List of positive integer factors of 68 that divides 68 without a remainder.
1,2,4,17,34,68
Factors of 49
List of positive integer factors of 49 that divides 49 without a remainder.
1,7,49
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 40
List of positive integer factors of 40 that divides 40 without a remainder.
1,2,4,5,8,10,20,40
Greatest Common Factor
We found the factors 68,49,84,40 . The biggest common factor number is the GCF number.
So the greatest common factor 68,49,84,40 is 1.
Lets's calculate LCM of 74,74,95,28
2 | 74, 74, 95, 28 |
37 | 37, 37, 95, 14 |
1, 1, 95, 14 |
∴ So the LCM of the given numbers is 2 x 37 x 1 x 1 x 95 x 14 = 98420
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/98420
Therefore, the GCF of Fractions 68/74,49/74,84/95,40/28 is 1/98420
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 74,74,95,28 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(74,74,95,28) = 1
common factors(in case of two or more numbers have common factors) = 148
GCF(74,74,95,28) x common factors =1 x 148 = 148
LCM(74,74,95,28) = ( 74 × 74 × 95 × 28 ) / 148
LCM(74,74,95,28) = 14566160 / 148
LCM(74,74,95,28) = 98420
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 68/74, 49/74, 84/95, 40/28?
Answer: GCF of Numerators as per given numbers 68/74, 49/74, 84/95, 40/28 is
GCF of Numerators i.e. for 68,49,84,40 is 1
LCM of denominators i.e. for 74,74,95,28 is 98420.
Thus, GCF of Fractions is 1/98420.Finally, GCF of Fractions for 68/74, 49/74, 84/95, 40/28 is 1/98420.